International Journal of Nonlinear Analysis and Applications

Fixed point of four maps in generalized b-metric spaces

Document Type : Research Paper

Author

Department of Sciences and Technology, Larbi Tebessi University-Tebessa, Algeria

Abstract

In this paper, some common fixed point results for four mappings satisfying generalized contractive condition in a generalized b-metric spaces are proved. Advantage of our work in comparison with studies done in the context of b-metric is that, the b-metric functions used in the theorems are not necessarily continuous. So, our results extend and improve several comparable results obtained previously. To show the validity of our work, we also prove that the same results hold even if the space is endowed with two metrics.

Keywords

[1] A. Aliouche, Common fixed point theorems via implicit relations, Miskolc Math. Notes 11(1) (2010) 3–12.
[2] A. Aliouche and T. Hamaizia, Common fixed point theorems for multivalued mappings in b-metric spaces with an application to integral inclusions, J. Anal. 2021 (2021) 1–20.
[3] H. Aydi, M. Bota, E. Karapinar and S. A Moradi, Common fixed point for weak ϕ-contractions on b-metric spaces, Fixed Point Theory 13(2) (2012) 337–346.
[4] I.A. Bakhtin, The contraction mapping principle in almost metric space, Funct. Anal, Unianowsk Gos. Ped. Inst. 30 (1989) 26–37.
[5] V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory 93 (1993) 3–9.
[6] M. Boriceanu, Fixed point theory on spaces with vector-valued b-metrics, Demonstratio Math. 42(4) (2009) 825–835.
[7] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena. 46(2) (1998) 263–276.
[8] L. Guran, M-F. Bota and A. Naseem, Fixed point problems on generalized metric spaces in Perov’s sense, Symmetry 12 (2020) 856.
[9] G.E. Hardy and T.D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16 (1973) 201–206.
[10] N. Hussain and M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011) 1677–1684.
[11] A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Differ. Uvavn. 2 (1964) 115–134.
[12] R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Model. 49 (2009) 703–708.
[13] J.R. Roshan, N. Shobkolaei, S. Sedghi and M. Abbas, Common fixed point of four maps in b-metric spaces, Hacettepe J. Math. Stat. 43(4) (2014) 613–624.
[14] M. Turinici, Finite-dimensional vector contractions and their fixed points, Studia Universitatis Babes-Bolyai Math. 35 (1990) 30–42.
[15] R.S. Varga, Matrix Iterative Analysis, Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2000.
[16] Z. Yanga, H. Sadatib, S. Sedghib and N. Shobec, Common fixed point theorems for non-compatible self-maps in b-metric spaces, J. Nonlinear Sci. App. 8 (2015) 1022–1031.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 2723-2730
  • Receive Date: 19 September 2021
  • Revise Date: 25 September 2021
  • Accept Date: 22 December 2021