Best proximity point results on \(\mathcal{R}\)-metric spaces with applications to fractional differential equation and production-consumption equilibrium

Volume 38, Issue 1, pp 45--55 https://dx.doi.org/10.22436/jmcs.038.01.04

Publication Date: November 21, 2024 Submission Date: August 21, 2024 Revision Date: September 25, 2024 Accteptance Date: October 10, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 530 Downloads
• 1775 Views

Authors

G. Janardhanan - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, Tamilnadu, India. G. Mani - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, Tamilnadu, India. Z. D. Mitrović - Faculty of Electrical Engineering, University of Banja Luka, Patre 5, Banja Luka, 78000, Bosnia and Herzegovina. A. Aloqaily - Department of Mathematics and Sciences, Prince Sultan University Riyadh, 1158, Saudi Arabia. N. Mlaiki - Department of Mathematics and Sciences, Prince Sultan University Riyadh, 1158, Saudi Arabia.

Abstract

In this article, we introduce the notion of best proximity point in \(\mathcal{R}\)-metric space. We prove the best proximity result in \(\mathcal{R}\)-metric space and also given some examples to strengthen our obtained results. Finally, an application to fractional differential equation and an application to production-consumption equilibrium are given.

Share and Cite

Keywords

• Fixed point
• fractional differential equation
• best proximity point
• dynamic market equilibrium problem
• \(\mathcal{R}\)-contraction
• \(\mathcal{R}\)-metric space

MSC

•  54H25
•  47H10
•  54E25

References

• [1] A. Abkar, M. Gabeleh, Best proximity points of non-self mappings, TOP, 21 (2013), 287–295
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] A. S. Anjum, C. Aage, Common fixed point theorem in F-metric spaces, J. Adv. Math. Stud., 15 (2022), 357–365
  • View Article
  • Google Scholar
  • MATH


• [3] M. Asadi, E. Karapınar, P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] M. I. Ayaria, H. Aydi, H. Hammouda, A best proximity point theorem for C-class-proximal non-self mappings and applications to an integro-differential system of equations, Filomat, 37 (2023), 4725–4742
  • View Article
  • MathSciNet
  • Google Scholar


• [5] S. S. Basha, Extensions of Banach’s contraction principle, Numer. Funct. Anal. Optim., 31 (2010), 569–576
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] S. S. Basha, Best proximity point theorems on partially ordered sets, Optim. Lett., 7 (2013), 1035–1043
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] S. S. Basha, N. Shahzad, R. Jeyaraj, Common best proximity points: global optimization of multi-objective functions, Appl. Math. Lett., 24 (2011), 883–886
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] M. Dhanraj, A. J. Gnanaprakasam, G. Mani, O. Ege, M. De la Sen, Solution to integral equation in an O-complete Branciari b-metric spaces, Axioms, 11 (2022), 1–14
  • View Article
  • Google Scholar


• [9] K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112 (1969), 234–240
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] A. George, P. Veeramani, On Some Result in Fuzzy Metric Space, Fuzzy Sets and Systems, 64 (1994), 395–399
  • View Article
  • MathSciNet
  • Google Scholar


• [11] S. K. Jain, G. Meena, D. Singh, J. K. Maitra, Best proximity point results with their consequences and applications, J. Inequal. Appl., 2022 (2022), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] M. Joshi, A. Tomar, T. Abdeljawad, On fixed points, their geometry and application to satellite web coupling problem in S−metric spaces, AIMS Math., 8 (2023), 4407–4441
  • View Article
  • MathSciNet
  • Google Scholar


• [13] E. Karapınar, ˙I. M. Erhan, Best proximity point on different type contractions, Appl. Math. Inf. Sci., 5 (2011), 558–569
  • View Article
  • Google Scholar


• [14] S. Khalehoghli, H. Rahimi, M. Eshaghi Gordji, Fixed point theorems in R-metric spaces with applications, AIMS Math., 5 (2020), 3125–3137
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] A. Latif, R. F. A Subaie, M. D. Alansari, Fixed points of generalized multi-valued contractive mappings in metric type spaces, J. Nonlinear Var. Anal., 6 (2022), 123–138
  • View Article
  • Google Scholar
  • MATH


• [16] G. Mani, A. J. Gnanaprakasam, O. Ege, A. Aloqaily, N. Mlaiki, Fixed point results in C∗-algebra-valued partial b-metric spaces with related application, Mathematics, 11 (2023), 9 pages
  • View Article
  • Google Scholar


• [17] G. Mani, G. Janardhanan, O. Ege, A. J. Gnanaprakasam, M. De la Sen, Solving a Boundary Value Problem via Fixed-Point Theorem on R-Metric Space, Symmetry, 14 (2022), 11 pages
  • View Article
  • Google Scholar


• [18] Z. Mustafa, V. Parvaneh, M. Abbas, J. R. Roshan, Some coincidence point results for generalized (y, f)-weakly contractive mappings in ordered G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages
  • View Article
  • Google Scholar


• [19] Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 26 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] K. Muthuvel, K. Kaliraj, K. S. Nisar, V. Vijayakumar, Relative controllability for ψ-Caputo fractional delay control system, Results Control Optim., 16 (2024), 16 pages
  • View Article
  • Google Scholar


• [21] K. S. Nisar, A constructive numerical approach to solve the Fractional Modified Camassa–Holm equation, Alex. Eng. J., 106 (2024), 19–24
  • View Article
  • Google Scholar


• [22] G. Poonguzali, V. Pragadeeswarar, M. De la Sen, Existence of Best Proximity Point in O-Complete Metric Spaces, Mathematics, 11 (2023), 9 pages
  • View Article
  • Google Scholar


• [23] V. Pragadeeswarar, G. Poonguzali, M. Marudai, S. Radenovi´c, Common best proximity theorem for multivalued mappings in partially ordered metric spaces, Fixed Point Theory Appl., 2017 (2017), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [24] J. B. Prolla, Fixed point theorems for set valued mappings and existence of best approximations, Numer. Funct. Anal. Optim., 5 (1983), 449–455
  • View Article
  • Google Scholar


• [25] A. Rezazgui, A. A. Tallafha, W. Shatanawi, Common fixed point results via Aν − α−contractions with a pair and two pairs of self-mappings in the frame of an extended quasi b-metric space, AIMS Math., 8 (2023), 7225–7241
  • View Article
  • MathSciNet
  • Google Scholar


• [26] V. M. Sehgal, S. P. Singh, A theorem on best approximations, Numer. Funct. Anal. Optim., 10 (1989), 181–184
  • View Article
  • MathSciNet
  • Google Scholar


• [27] W. Shatanawi, T. A. M. Shatnawi, New fixed point results in controlled metric type spaces based on new contractive conditions, AIMS Math., 8 (2023), 9314–9330
  • View Article
  • Google Scholar


• [28] A. A. Thirthar, H. Abboubakar, A. L. Alaoui, K. S. Nisar, Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions, Results Control Optim., 16 (2024), 21 pages
  • View Article
  • Google Scholar