A common fixed point result for two pairs of maps in b-metric spaces without (E.A.)-property

• Main Author: Akkouchi Mohamed
• Format: Article
• Language: English
• Published: University of Kragujevac, Faculty of Technical Sciences Čačak, Serbia 2019-01-01
• Series: Mathematica Moravica
• Subjects: b-metric spaces; common fixed point for four maps; weakly compatible maps; compatible maps; property (e.a.); well-posedness
• Online Access: https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2019/1450-59321902029A.pdf

In this paper, we investigate a common fixed point problem for two pairs {f, S} and {g, T} of weakly compatible selfmaps of a complete b-metric (X, d; s), satisfying a contractive condition of Ćirić type. This contraction and some of its variants were used in the paper [29] published in 2016 by V. Ozturk and S. Radenovic, requiring the (E.A.)-property for the pairs {f, S} and {g, T}. The aim of this paper is to provide some improvements to the main result of [29]. Our main theorem will improve certain results published in 2015, by V. Ozturk and D. Turkoglu (see [30] and [31]). We improve also results from other related papers (see the references herin). Indeed, we remove the (E.A.)property and weaken certain assumptions imposed in these papers. So, our work aims to extend and unify, in one go, several common fixed point results known in a recent literature. We furnish two illustrative examples and we prove that the fixed point problem, considered here, for the pairs {f, S} and {g, T} is well-posed. We compare our main result with a recent result obtained in 2018 by N. Hussain, Z. D. Mitrović and S. Radenović in [19].