International Journal of Nonlinear Analysis and Applications

New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations

Document Type : Research Paper

Authors

Equipe de Recherche en Mathematiques Appliquees, Technologies de l’Information et de la Communication Faculte Polydisciplinare de Khouribga, Universite Sultan Moulay Slimane de Beni-Mellal, Morocco

Abstract

In this paper, we prove a new common fixed point in a general topological space with a $\tau-$distance. Then we deduce two common fixed point theorems for two new classes of contractive selfmappings in complete bounded metric spaces. Moreover, an application to a system of differential equations is given.

Keywords

[1] M. Aamri and D. El Moutawakil, τ -distance in general topological spaces with application to fixed point theory, Southwest J. Pure Appl. Math. 2 (2003) 1–5.
[2] H. Baghani, M. Eshaghi Gordji and M. Ramezani, Orthogonal sets, the axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl. 18 (2016) 465–477.
[3] L. Ciric, Some Recent Results in Metrical Fixed Point Theory, University of Belgrade, Serbia, 2003.
[4] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962) 74-–79.
[5] D. Djoric, Common fixed point for generalized (ψ, φ)-weak contractions, Appl. Math. Lett. 22 (2009) 1896–1900.
[6] M.E. Gordji, M. Rameani, M. De La Sen and Y. Je Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory 18(2) (2017) 569–578.
[7] M.E. Gordji and H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Top. Alg. 6(3) (2017) 251–260.
[8] G. Jungck and B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29(3) (1998) 227–238.
[9] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, Fixed point theorems in R-metric spaces with applications, AIMS Math. 5(4) (2020) 3125–3137.
[10] W. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces, Springer International Publishing Switzerland, 2014.
[11] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl. 8(2) (2017) 23–28.
[12] V.V. Nemytzki, The fixed point method in analysis, (Russian), Usp. Mat. Nauk 1 (1936) 141–174.
[13] S. Radenovic, Z. Kadelburg, D. Jandrlic and A. Jandrlic, Some results on weak contraction maps, Bull. Iran. Math. Soc. 38 (2012) 625–645.
[14] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001) 2683–2693.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 903-911
  • Receive Date: 08 September 2020
  • Revise Date: 13 March 2021
  • Accept Date: 13 March 2021