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Best proximity points of admissible almost generalized weakly contractive mappings with rational expressions on b-metric spaces
Best proximity points of admissible almost generalized weakly contractive mappings with rational expressions on b-metric spaces
en
en
The aim of this paper is to introduce almost generalized proximal \((\alpha-\psi-\varphi-\theta)\)-weakly contractive mappings with rational expressions and prove the best proximity point theorems for such mappings. The main results of this
paper are generalizations of several comparable results in the literature.
97
109
Lakshmi Narayan
Mishra
Department of Mathematics, School of Advanced Sciences
Vellore Institute of Technology (VIT) University
India
Vinita
Dewangan
Govt. S.N. College Nagari Distt.-Dhamtari
India
Vishnu Narayan
Mishra
Dept. of Mathematics
Indira Gandhi National Tribal University
India
vishnunarayanmishra@gmail.com
Seda
Karateke
Department of Mathematics and Computer Science, Faculty of Science and Letters
Istanbul Arel University
Turkey
Fixed point
best proximity points
metric space
\(b\)-metric space
admissible mapping
Article.1.pdf
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P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-8
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N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly $(\psi, \varphi, L, A, B)$-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013 (2013), 1-18
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H. Işık, H. Aydi, N. Mlaiki, S. Radenović, Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application, Axioms, 8 (2019), 1-12
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H. Işık, M. S. Sezen, C. Vetro, $\varphi$-Best proximity point theorems and applications to variational inequality problems, J. Fixed Point Theory Appl., 19 (2017), 3177-3189
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E. Karapinar, P. Kumam, P. Salimi, On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
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E. Karapinar, V. Pragadeeswarar, M. Marudai, Best proximity point for generalized proximal weak contractions in complete metric space, J. Appl. Math., 2014 (2014), 1-6
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M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
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W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851-862
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P. Kumam, N. V. Dung, V. T. L. Hang, Some equivalences between cone $b$-metric spaces and b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-8
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P. Kumam, P. Salimi, C. Vetro, Best proximity point results for modified $\alpha$-proximal C-contraction mappings, Fixed Point Theory Appl., 2014 (2014), 1-16
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X.-L. Liu, M. Zhou, L. N. Mishra, V. N. Mishra, B. Damjanović, Common fixed point theorem of six self-mappings in Menger spaces using $(CLR_{ST})$ property, Open Math., 16 (2018), 1423-1434
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L. N. Mishra, On existence and behavior of solutions to some nonlinear integral equations with applications, Ph.D. Thesis (National Institute of Technology), India (2017)
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L. N. Mishra, K. Jyoti, A. Rani Vandana, Fixed point theorems with digital contractions image processing, Nonlinear Sci. Lett. A, 9 (2018), 104-115
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L. N. Mishra, S. K. Tiwari, V. N. Mishra, Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces, J. Appl. Anal. Comput., 5 (2015), 600-612
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L. N. Mishra, S. K. Tiwari, V. N. Mishra, I. A. Khan, Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces, J. Funct. Spaces, 2015 (2015), 1-8
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H. K. Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 2013 (2013), 1-11
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V. Pragadeeswarar, M. Marudai, Best proximity points for generalized proximal weak contractions satisfying rational expression on ordered metric spaces, Abstr. Appl. Anal., 2015 (2015), 1-6
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V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), 4804-4808
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J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized $(\psi, \phi){s}$-contractive mappings in ordered $b$-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-23
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B. Samet, C. Vetro, P. Vetro, Fixed point theorem for $\alpha-\psi$-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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W. Sanhan, C. Mongkolkeha, P. Kumam, Generalized proximal $\phi$-contraction mappings and Best proximity points, Abstr. Appl. Anal., 2012 (2012), 1-19
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W. Shatanawi, A. Pitea, R. Lazović, Contraction conditions using comparison functions on $b$-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
]
Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\)
Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\)
en
en
This study establishes a novel nonexistence result for a strongly coupled viscoelastic system with Balakrishnan-Taylor damping and a nonlinear source in the whole space. Sufficient conditions ensuring the nonexistence of solutions are established using the test function method.
110
118
Mourad
Benzahi
Department of Mathematics and Computer Science, LAMIS Laboratory
Larbi Tebessi University
Algeria
mourad.benzahi@univ-tebessa.dz
Abdelrahmane
Zarai
Department of Mathematics and Computer Science, LAMIS Laboratory
Larbi Tebessi University
Algeria
abderrahmane.zarai@univ-tebessa.dz
Salem
Abdelmalek
Department of Mathematics and Computer Science, LAMIS Laboratory
Larbi Tebessi University
Algeria
salem.abdelmalek@univ-tebessa.dz
Samir
Bendoukha
Electrical Engineering Department, College of Engineering at Yanbu
Taibah University
Saudi Arabia
sbendoukha@taibahu.edu.sa
Balakrishnan-Taylor system
non-solvability
memory term
Article.2.pdf
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]
New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation
New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation
en
en
In this paper, new group iterative schemes are developed for the numerical solution of two-dimensional anomalous fractional sub-diffusion equation subject to specific initial and Dirichlet boundary conditions. The new group relaxation iterative schemes are derived from the combination of standard and rotated (skewed) five-point modified implicit finite difference approximations. The results derived from the conducted numerical experiments show that fractional explicit de-coupled group (FEDG) iterative method has a significantly less computational cost in terms of CPU-timings as compared to the other iterative schemes, without threatening compromising accuracies.
119
127
Ajmal
Ali
Department of Mathematics
Virtual University of Pakistan
Pakistan
ajmal@vu.edu.pk
Muhammad
Abbas
Departemnt of Mathematics
University of Sargodha
Pakistan
muhammad.abbas@uos.edu.pk
Tayyaba
Akram
School of Mathematical Sciences
Universiti Sains Malaysia
Malaysia
Riemann-Liouville fractional derivative
fractional implicit standard point
fractional implicit rotated point
anomalous fractional sub-diffusion equation
Article.3.pdf
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[1]
A. Ali, N. H. M. Ali, On numerical solution of muti-terms fractional differential equations using shifted Chebyshev polynomials, Int. J. Pur. Appl. Math., 120 (2018), 11-125
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A. Ali, N. H. M. Ali, On numerical solution of fractional order delay differential equation using Chebyshev collocation method, New Trends in Math. Sci., 6 (2018), 8-17
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A. Ali, N. H. M. Ali, Explicit group iterative methods in the solution of two dimensional time fractional diffusion wave equation, Compusoft, 7 (2018), 2931-2938
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A. Ali, N. H. M. Ali, New group fractional damped wave iterative solvers using mathematica, International Conference on Mathematical Sciences and Technology (AIP Conference Proceedings, Penang, Malaysia), 2018 (2184), 1-10
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A. Ali, N. H. M. Ali, Explicit group iterative methods for the solution of two-dimensional time-fractional telegraph equation, The 4th Innovation and Analytics Conference and Exhibition (AIP Conference Proceedings, Sintok Kedah, Malaysia), 2138 (2019), 1-6
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A. Ali, N. H. M. Ali, On skewed grid point iterative method for solving 2D hyperbolic telegraph fractional differential equation, Adv. Difference Equ., 2019 (2019), 1-29
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M. Amin, M. Abbas, M. K. Iqbal, D. Baleanu, Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations, Adv. Difference Equ., 2019 (2019), 1-22
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M. Amin, M. Abbas, M. K. Iqbal, A. I. M. Ismial, D. Baleanu, A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations, Adv. Difference Equ., 2019 (2019), 1-21
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N. A. Asif, Z. Hammouch, M. B. Riaz, H. Bulut, Analytical solution of a Maxwell fluid with slip effects in view of the Caputo-Fabrizio derivative, Eur. Phys. J. Plus, 133 (2018), 1-13
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A. T. Balasim, N. H. M. Ali, Group iterative methods for the solution of two-dimensional time-fractional diffusion equation, Advances in Industrial and Applied Mathematics (AIP Conference Proceedings, Johor Bahru, Malaysia), 2016 (1750), 1-7
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A. T. Balasim, N. H. M. Ali, The solution of 2-D time-fractional diffusion equation by the fractional modified explicit group iterative method, International Conference on Mathematics, Engineering and Industrial Applications (AIP Conference Proceedings, Songkhla, Thailand), 1775 (2016), 1-8
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A. T. Balasim, N. H. M. Ali, New group iterative schemes in the numerical solution of the two-dimensional time fractional advection-diffusion equation, Cogent Math., 4 (2017), 1-19
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C.-M. Chen, F. Liu, I. Turner, V. Anh, Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation, Numer. Algorithms, 54 (2010), 1-21
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R. Hilfer, Application of fractional Calculus in Physics, World Scientific Publishing Co., River Edge (2000)
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N. Khalid, M. Abbas, M. K. Iqbal, Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms, Appl. Math. Comput., 349 (2019), 393-407
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N. Khalid, M. Abbas, M. K. Iqbal, D. Baleanu, A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic $B$-spline functions, Adv. Difference Equ., 2020 (2020), 1-22
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Y. F. Li, D. L. Wang, Improved efficient difference method for the modified anomalous sub-diffusion equation with a nonlinear source term, Int. J. Comput. Math., 94 (2017), 821-840
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K. L. Ming, N. H. M. Ali, New explicit group iterative methods in the solution of three dimensional hyperbolic telegraph equations, J. Comput. Phys., 294 (2015), 382-404
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M. B. Riaz, M. A. Imran, K. Shabbir, Analytic solutions of Oldroyd-B fluid with fractional derivatives in a circular duct that applies a constant couple, Alex. Eng. J., 55 (2016), 3267-3275
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M. B. Riaz, A. A. Zafar, Exact solutions for the blood flow through a circular tube under the influence of a magnetic field using fractional Caputo-Fabrizio derivatives, Math. Model. Nat. Phenom., 13 (2018), 1-12
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I. M. Sokolov, J. Klafter, From diffusion to anomalous diffusion: acentury after Einsteins Brownian motion, Chaos, 15 (2005), 26-103
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P. J. Torvik, R. L. Bagley, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech., 51 (1984), 294-298
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]
Some remarks concerning \(D^{*}\)-metric spaces
Some remarks concerning \(D^{*}\)-metric spaces
en
en
In [S. Sedghi, N. Shobe, H. Y. Zhou, Fixed Point Theory Appl., {\bf 2007} (2007), 13 pages], Sedghi et al. introduced the notion of \(D^{*}\)-metric space and in [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, \(\bf 64\) (2012), 258--266] the authors claimed that every \(G\)-metric space is \(D^{*}\)-metric. In this short paper we present examples to show that \(D^{*}\)-metric need not be \(G\)-metric as well as the \(G\)-metric need not be \(D^{*}\)-metric.
128
130
Zead
Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
zead@qu.edu.qa
M. M. M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
Metric space
\(D^{*}\)-metric space
\(G\)-metric space
Article.4.pdf
[
[1]
M. M. M. Jaradat, Z. Mustafa, S. U. Khan, M. Arshad, J. Ahmad, Some fixed point results on $G$-metric and $G_b$-metric spaces, Demonstr. Math., 50 (2017), 190-207
##[2]
S. U. Khan, J. Ahmad, M. Arshad, T. Rasham, Some new fixed point theorems in $C^*$-algebra valued $G_b$-metric spaces, J. Adv. Math. Stud., 12 (2019), 22-29
##[3]
Z. Mustafa, Some new common fixed point theorems under strict contractive conditions in $G$-metric spaces, J. Appl. Math., 2012 (2012), 1-21
##[4]
Z. Mustafa, M. Arshad, S. U. Khan, J. Ahmad, M. M. M. Jaradat, Common fixed point for multivalued mappings in G-metric spaces with applications, J. Nonlinear Sci. Appl., 10 (2017), 2550-2564
##[5]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
##[6]
S. Sedghi, N. Shobe, Common Fixed Point Theorems for two mappings in $D^{*}$-Metric Spaces, Math. Aeterna, 2 (2012), 89-100
##[7]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point in $S$-metric spaces, Mat. Vesnik, 64 (2012), 258-266
##[8]
S. Sedghi, N. Shobe, H. Y. Zhou, A common fixed point theorem in $D^{*}$-metric spaces, Fixed Point Theory Appl., 2007 (2007), 1-13
]
The Jensen's inequality and functional form of Jensen's inequality for 3-convex functions at a point
The Jensen's inequality and functional form of Jensen's inequality for 3-convex functions at a point
en
en
In this paper, we give the refinement of extension of Jensen's inequality to affine combinations. Furthermore, we present a functional form of Jensen's inequality for continuous 3-convex functions at a point of one variable.
131
141
Yu Ming
Chu
Department of Mathematics
Huzhou University
China
Imran Abbas
Baloch
Abdus Salam School of Mathematical Sciences GC University
Higher Education Department
Govt. College Gulberg Lahore
Pakistan
Pakistan
iabbasbaloch@gmail.com
Absar Ul
Haq
Department of Natural Sciences and Humanities
University of Engineering and Technology (Narowal Campus)
Pakistan
Manuel De La
Sen
Institute of Research and Development of Processors
University of the Basque Country campus of Leioa (Bizkaia)
Spain
Affine combination
positive linear functional
convex function
preinvex function
Jensen's inequality
Article.5.pdf
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[1]
I. A. Baloch, J. Pečarić, M. Praljak, Generalization of Levinson's inequality, J. Math. Inequal., 9 (2015), 571-586
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C. P. Niculescu, L.-E. Persson, Convex functions and their applications, Springer-Verlag, New York (2006)
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Z. Pavić, Generalization of the Functional form of Jensen's inequality, J. Adv. Inequal. Appl., 2014 (2014), 1-12
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Z. Pavić, Certain inequalities for convex functions, J. Math. Inequal., 9 (2015), 1349-1364
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J. E. Pečarić, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston (1991)
]
Fuzzy soft Hilbert spaces
Fuzzy soft Hilbert spaces
en
en
In this work, we define the fuzzy soft Hilbert space \(\tilde{H}\) based on the definition of the fuzzy soft inner product space \((\tilde{U},\widetilde{<\cdot,\cdot>})\), introduced by Faried {et al.} [{N. Faried, M. S. S. Ali, H. H. Sakr, Appl. Math. Inf. Sci., {\bf 14} (2020), 709--720}], in terms of the fuzzy soft vector \(\tilde{v}_{f_{G(e)}}\). Moreover, we show that \(\mathbb{C}^{n}(A)\), \(\mathbb{R}^{n}(A)\) and \(\ell_{2}(A)\) are suitable examples of fuzzy soft Hilbert spaces. In addition, it is proved that the fuzzy soft orthogonal complement of any non-empty fuzzy soft subset of \(\tilde{H}\) is a fuzzy soft closed fuzzy soft subspace of \(\tilde{H}\) and we study some of the fuzzy soft Hilbert spaces properties and some of the fuzzy soft inner product spaces properties. Furthermore, we introduce the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Moreover, we present the fuzzy soft Bessel's inequality and the fuzzy soft Parseval's formula in this generalized setting.
142
157
Nashat
Faried
Department of Mathematics, Faculty of Science
Ain Shams University
Egypt
Mohamed S.S.
Ali
Department of Mathematics, Faculty of Education
Ain Shams University
Egypt
Hanan H.
Sakr
Department of Mathematics, Faculty of Education
Ain Shams University
Egypt
hananhassan@edu.asu.edu.eg
Fuzzy set
fuzzy soft Hilbert space
fuzzy soft inner product space
fuzzy soft linear space
fuzzy soft set
soft set
Article.6.pdf
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S. Bayramov, C. Gunduz, Soft locally compact spaces and soft paracompact spaces, J. Math. Sys. Sci., 3 (2013), 122-130
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T. Beaula, C. Gunaseeli, On fuzzy soft metric spaces, Malaya J. Mat., 2 (2014), 197-202
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T. Beaula, M. M. Priyanga, A new notion for fuzzy soft normed linear space, Int. J. Fuzzy Math. Arch., 9 (2015), 81-90
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T. Beaula, M. M. Priyanga, Fuzzy soft linear operator on fuzzy soft normed linear spaces, Int. J. App. Fuzzy Sets Art. Intell., 6 (2020), 73-92
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S. Das, S. K. Samanta, On soft inner product spaces, Ann. Fuzzy Math. Inform., 6 (2013), 151-170
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S. Das, S. K. Samanta, Soft Metric, Ann. Fuzzy Math. Inform., 6 (2013), 77-94
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N. Faried, M. S. S. Ali, H. H. Sakr, Fuzzy soft inner product spaces, Appl. Math. Inf. Sci., 14 (2020), 709-720
##[8]
C. Gunaseeli, Some Contributions to Special Fuzzy Topological Spaces, Ph.D. Thesis (Bharathidasan University), India (2012)
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K. Hayat, M. I. Ali, J. C. R. Alcantud, B.-Y. Cao, K. U. Tariq, Best concept selection in design process: An application of generalized intuitionistic fuzzy soft sets, J. Intell. Fuzzy Syst., 35 (2018), 5707-5720
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A. Z. Khameneh, A. Kiliçman, A. R. Salleh, Parameterized norm and parameterized fixed-point theorem by using fuzzy soft set theory, arXiv, 2013 (2013), 1-15
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J. Mahanta, P. K. Das, Fuzzy soft topological spaces, J. Intell. Fuzzy Syst., 32 (2017), 443-450
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T. Mahmood, M. I. Ali, M. A. Malik, W. Ahmed, On lattice ordered intuitionistic fuzzy soft sets, Int. J. Algebra Stat., 7 (2018), 46-61
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P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic fuzzy soft sets, J. Fuzzy Math., 9 (2001), 677-692
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P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562
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D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19-31
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T. J. Neog, D. K. Sut, G. C. Hazarika, Fuzzy soft topological spaces, Int. J. Latest Trend Math., 2 (2012), 54-67
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N. Sultana, N. Rani, M. I. Ali, A. Hussain, Soft translations and soft extensions of BCI/BCK-algebras, Sci. World J., 2014 (2014), 1-6
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M. I. Yazar, C. G. Aras, S. Bayramov, Results on soft Hilbert spaces, TWMS J. App. Eng. Math., 9 (2019), 159-164
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Robust and efficient finite element multigrid and preconditioned minimum residual solvers for the distributed elliptic optimal control problems
Robust and efficient finite element multigrid and preconditioned minimum residual solvers for the distributed elliptic optimal control problems
en
en
In this study, the optimal control problem is considered. This is an important class of partial differential equations constrained optimization problems. The constraint here is an elliptic partial differential equation with Neumann boundary conditions. The discretization of the optimality system produces a block coupled algebraic system of equations of saddle point form. The solution of such systems is a major computational task since they require specialized methods. Constructing robust, fast and efficient solvers for their numerical solution has preoccupied the computational science community for decades and various approaches have been developed. The approaches involve solving simultaneously for all the unknowns using a coupled block system, the segregated approach where a reduced system is solved and the approach of reducing to a fixed point form. Here the minimum residual solver with ideal preconditioning is applied to the unreduced 3 by 3 and reduced 2 by 2 coupled systems and compared to the multigrid method applied to the compact fixed-point form. The two methods are compared numerically in terms of iterative counts and computational times. The numerical results indicate that the two methods produce similar outcomes and the multigrid solver becoming very competitive in terms of the iterative counts though slower than preconditioned minimum residual solver in terms of computational times. For all the approaches, the two methods exhibited mesh and parameter independent convergence. The optimal performance of the two methods is verified computationally and theoretically.
158
173
Kizito
Muzhinji
Department of Mathematics and Applied Mathematics
University of Venda
South Africa
kizito.muzhinji@univen.ac.za
Elliptic optimal control problems
partial differential equations (PDEs)
saddle point problems
optimality system
finite element method (FEM)
multigrid method (MGM)
preconditioned minimum residual method (PMINRES)
Article.7.pdf
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Computing the edge metric dimension of convex polytopes related graphs
Computing the edge metric dimension of convex polytopes related graphs
en
en
Let \(G=(V(G),E(G))\) be a connected graph and \(d(f,y)\) denotes the distance between edge \(f\) and vertex \(y\), which is defined as \(d(f,y) = \min \{d(p,y),d(q,y)\}\), where \(f=pq\). A subset \(W_E \subseteq V(G)\) is called an edge metric generator for graph \(G\) if for every two distinct edges \(f_1, f_2 \in E(G)\), there exists a vertex \(y\in W_E\) such that \(d(f_1,y) \neq d(f_2,y)\). An edge metric generator with minimum number of vertices is called an edge metric basis for graph \(G\) and the cardinality of an edge metric basis is called the edge metric dimension represented by \(edim(G)\). In this paper, we study the edge metric dimension of flower graph \({f}_{n\times 3}\) and also calculate the edge metric dimension of the prism related graphs \(D_{n}^{'}\) and \(D_{n}^{t}\). It has been concluded that the edge metric dimension of \(D_{n}^{'}\) is bounded, while of \({f}_{n\times 3}\) and \(D_{n}^{t}\) is unbounded.
174
188
Muhammad
Ahsan
Department of Mathematics
University of Management and Technology
Pakistan
muhammadahsanm@gmail.com
Zohaib
Zahid
Department of Mathematics
University of Management and Technology
Pakistan
Sohail
Zafar
Department of Mathematics
University of Management and Technology
Pakistan
Arif
Rafiq
Department of Mathematics
Virtual University of Pakistan (VU)
Pakistan
Muhammad Sarwar
Sindhu
Department of Mathematics
Virtual University of Pakistan (VU)
Pakistan
Muhammad
Umar
Department of Mathematics
Virtual University of Pakistan (VU)
Pakistan
Edge metric dimension
edge metric generator
edge metric basis
resolving set
prism related graphs
flower graph
Article.8.pdf
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]