International Journal of Nonlinear Analysis and Applications

Best proximity point theorems for generalized weakly contractive mappings in metric spaces

Document Type : Research Paper

Authors

Department of Mathematics, College of Natural Science and Computational, Wolkite University, Wolkite, Ethiopia

Abstract

The aim of this paper is to establish certain new classes of proximal contraction mappings and establish some best
proximity point theorems for such kinds of mapping, thereby we extend some fixed point theorems for generalized
weakly contractive mappings in metric spaces to the case of non-self mapping.

Keywords

[1] Ya.I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and Its Applications (Basel) (I. Gohberg and Yu. Lyubich, eds.), Birkhauser Basel 1997, pp. 7–22.
[2] J. Bae and S.H. Cho, Fixed points of weak α-contraction type maps, Fixed Point Theory Appl. 2014 (2014), no. 1, 175.
[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), no. 1, 133–181.
[4] S. Binayak, Choudhury, P. Konar, B.E. Rhoades, and N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal. 74 (2011), no. 6, 2116–2126.
[5] S. Cho, Fixed point theorems for generalized weakly contractive mappings in metric spaces with applications, J. Fixed Point Theory Appl. 2018 (2018), no. 3, 1687–1812.
[6] M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 1 (1962), no. 1, 74–79.
[7] M.S Khan, M Swaleh, and S Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), no. 1, 1–9.
[8] Z. Mitrovic, A. Dinmohammadi, V. Parvaneh, and E. Jakupovic, Best approximation for multivalued mappings in para normed spaces, J. Interdiscip. Math. 24 (2021), no. 6, 1617–1625.
[9] S. Mondal and L.K. Dey, Some common best proximity point theorems in a complete metric space, Afr. Mat. 28 (2017), 85–97.
[10] V. Parvaneh M.R. Haddadi, and M. Moursalian, Global optimal approximate solutions of best proximity points, Filomat 35 (2021), no. 5, 1555–1564.
[11] V. Parvaneh, B. Mohammadi, and H. Aydi, On extended interpolative  Ciric–Reich–Rus type F-contractions and an application, J. Inequal. Appl. 2019 (2019), 1–11.
[12] A. Razanii, M. Abbas, and V. Parvaneh, Periodic points of t-Ciric generalized contraction mappings in ordered metric spaces, Georgian Math. J. 19 (2012), no. 4, 597–610.
[13] Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001) no. 4 2683–2693.
[14] J.R. Roshan, Z. Kadelburg, Z. Mustafa, V. Parvaneh, b2-metric spaces and some fixed point theorems, J. Fixed Point Theory Appl. 2014 (2014), no. 1, 1–23.
[15] S. Sadiq Basha, Best proximity point theorems generalizing the contraction principle, Nonlinear Anal. 74 (2011) no. 17, 5844–5850.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 10
October 2023
Pages 293-302
  • Receive Date: 12 August 2022
  • Revise Date: 05 June 2023
  • Accept Date: 16 June 2023