International Journal of Nonlinear Analysis and Applications

Fixed point theorems for weakly contractive mapping on generalized asymmetric metric spaces

Document Type : Research Paper

Authors

1 LaSMA Laboratory Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P. O. Box 1796 Fez Atlas, Morocco

2 Laboratory of Analysis, Modeling and Simulation Faculty of Sciences Ben M’Sik, Hassan II University, B.P. 7955 Casablanca, Morocco

3 Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, P. O. Box 133 Kenitra, Morocco

4 Department of Data Science, Daejin University, Kyunggi 11159, Korea

Abstract

In this present paper, inspired by the concept of weakly contractive mapping in metric spaces, we introduce the concept of weakly contractive mapping in generalized asymmetric metric spaces and we establish various fixed point theorems for such mappings in complete generalized metric spaces.

Keywords

[1] A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl. 1 (2008), 45–48.
[2] S. Banach, Sur les operations dans les ensembles abstraits et leur applications integrales, Fund. Math. 3 (1922), 133–181.
[3] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. (Debr.) 57 (2000), 31–37.
[4] F.E. Browder, On the convergence of successive approximations for nonlinear functional equations, Indag. Math. 30 (1968), 27–35.
[5] M. Jleli, E. Karapinar, and B. Samet, Further generalizations of the Banach contraction principle, J. Inequal. Appl. 2014 (2014), Paper No. 439.
[6] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014 (2014), Paper No. 38.
[7] R. Kannan, Some results on fixed points-II, Amer. Math. Month. 76 (1969), 405–408.
[8] A. Kari, M. Rossafi, E. Marhrani, and M. Aamri, Fixed-point theorem for nonlinear F-contraction via w-distance, Adv. Math. Phys. 2020 (2020), Article ID 6617517.
[9] A. Kari, M. Rossafi, E. Marhrani, and M. Aamri, New fixed point theorems for θ − ϕ-contraction on complete rectangular b-metric spaces, Abstr. Appl. Anal. 2020 (2020), Article ID 8833214.
[10] A. Kari, M. Rossafi, E. Marhrani, and M. Aamri, Fixed-point theorems for θ − ϕ-contraction in generalized asymmetric metric spaces, Int. J. Math. Math. Sci. 2020 (2020), Article ID 8867020.
[11] 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.
[12] W.A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl. 2013 (2013), Paper No. 129.
[13] H. Lakzian and B. Samet, Fixed point for (ψ, ϕ)-weakly contractive mappings in generalized metric spaces, Appl. Math. Lett. 25 (2012), no. 5, 902–906.
[14] H. Piri, S. Rahrovi, and Zarghami, Some fixed point theorems on generalized asymmetric metric spaces, Asian-Eur. J. Math. 14 (2021), no. 7, Article ID 2150109.
[15] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124.
[16] B. Samet, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal. 3 (2009), 25–28.
[17] B. Samet, Discussion on a fixed point theorem of Banach-Cacciopli type on a class of generalized metric spaces, Publ. Math. Debrecen 76 (2010), 493–494.
[18] I.R. Sarma, J.M. Rao, and S.S. Rao, Contractions over-generalized metric spaces, J. Nonlinear. Sci. Appl. 2 (2009), 180–182.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 5
May 2025
Pages 129-142
  • Receive Date: 21 April 2022
  • Revise Date: 08 July 2022
  • Accept Date: 07 August 2022