Best proximity point results for generalized proximal $Z$-contraction mappings in metric spaces and some applications
Resumo
In this paper, we define generalized proximal Z-contraction mappings of first and second kind in a metric space (X, d). The existence of best proximity point is shown for the defined mappings under some specific conditions which generalizes and extends some existing results of Olgun et al. [23] and Abbas et al. [1]. Suitable examples are given to justify the derived results. Some applications are also shown via fixed point formulation for such mappings in variational inequality problem and homotopy result.
Downloads
Referências
M. Abbas and Y. I. Suleiman and C. Vetro, A simulation function approach for best proximity point and variational inequality problems, Miskolc Mathematical Notes 18 (1), 1–16, (2017).
R. P. Agarwal and J. Dshalalow and D. O’Regan, Fixed point and homotopy results for generalized contractive maps of Reich type, Applicable Analysis 82(4), 329-350, (2003).
A. E. Al-Mazrooei and A. Hussain and M. Ishfaq and J. Ahmad, Simulative Suzuki-Gerghaty type contraction with C -class functions and applications, IEEE Access 7, 75284–75291, (2009).
M. A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis: Theory, Methods and Applications 70(10), 3665-3671, (2009).
D. R. Babu, G. V. R. Babu, Fixed points of Suzuki Z-contraction type maps in b-metric spaces, Advances in the Theory of Nonlinear Analysis and its Application 4(1), 14–28, (2020).
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae 3(1), 133-181, (1922).
S. S. Basha, Best proximity point theorems, Journal of Approximation Theory 163(11), 1772-1781, (2011).
A. Bnouhachem and M. A. Noor, A new iterative method for variational inequalities, Applied Mathematics and Computation 182(2), 1673-1682, (2006).
A. R. Butt and I. Beg and A. Iftikhar, Fixed points on ordered metric spaces with applications in homotopy theory, Journal of Fixed Point Theory and Applications 20(1), 1-15, (2018).
F. Deutsch, Best Approximation in Inner Product Spaces, New York: Springer-Verlag 21-32, (2001).
Y. Elkouch and E. M. Marhrani, On some fixed point theorems in generalized metric spaces, Fixed Point Theory and Applications 23, 1-17, (2017).
N. Goswami and R. Roy and V. N. Mishra and L. M. Ruiz, Common best proximity point results for T-GKT cyclic ϕ-contraction mappings in partial metric spaces with some applications, Symmetry 13(6), 1-13, (2021).
N. Goswami and R. Roy, Some coupled best proximity point results for weak GKT cyclic ϕ-contraction mappings on metric spaces, Proceedings of the Jangjeon Mathematical Society 4(4), 485-502, (2020).
N. Haokip and N. Goswami, Some fixed point theorems for generalized Kannan type mappings in b-metric spaces, Proyecciones (Antofagasta) 38(4), 763-782, (2019).
E. Karapınar, Fixed points results via simulation functions, Filomat 30(8), 2343-2350, (2016).
Z. A. Khan and I. Ahmad and K. Shah, Applications of fixed point theory to investigate a system of fractional order differential equations, Journal of Function Spaces 1-7, (2021).
F. Khojasteh and S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29(6), 1189-1194, (2015).
A. Kostic and V. Rakocevic and S. Radenovic, Best proximity points involving simulation functions with w0-distance, Revista De La Real Academia De Ciencias Exactas, Fısicas Y Naturales. Serie A. Matematicas 113(2), 715-727, (2018).
P. Kumam and D. Gopal and L. Budhiya, A new fixed point theorem under Suzuki type Z-contraction mappings, Journal of Mathematical Analysis 1(8), 113-119, (2017).
J. T. Markin, Homotopic invariance of fixed points in hyperconvex metric spaces, Topology and Its Applications 130(2), 111-114, (2003).
Z. Ma and A. Hussain and M. Adeel and N. Hussain and E. Savas , Best proximity point results for generalized Θ-contractions and application to matrix equations, Symmetry 11(1), 1-20, (2019).
M. A. Noor, Extended general variational inequalities, Applied Mathematics Letters 22(2), 182-186, (2009).
M. Olgun and O. Bi，cer and T. Alyildiz, A new aspect to Picard operators with simulation functions, Turkish Journal of Mathematics 40, 832-837, (2016).
A. Padcharoen and P. Kumam and P. Saipara and P. Chaipunya, Generalized Suzuki type Z-contraction in complete metric spaces, Kragujevac Journal of Mathematics 42(3), 419-430, (2018).
Y. Su and J. C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory and Applications 120(1), 1-13, (2015).
G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, Academie des Sciences de Paris 258, 4413–4416, (1964).
F. Tchier and C. Vetro and F. Vetro, Best approximation and variational inequality problems involving a simulation function, Fixed Point Theory and Applications 26, 1-15, (2016).
B. C. Tripathy and S. Paul and N. R. Das, Banach’s and Kannan’s fixed point results in fuzzy 2-metric spaces, Proyecciones (Antofagasta), 32(4), 359–375, (2013).
B. C. Tripathy and S. Paul and N. R. Das, A fixed point theorem in a generalized fuzzy metric space, Boletim da Sociedade Paranaense de Matemática, 32(2), 221-227, (2014).
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
