Common Fixed Point Results for a Pair of Multivalued Mappings in Complex-Valuedb-Metric Spaces

Olawale Kazeem Oyewole,Kazeem Olalekan Aremu,Lateef Olakunle Jolaoso

doi:10.1155/2020/9738971

Abstract

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valuedb-metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation.

Highlights

Fixed point theory is a well-researched area of mathematics; in particular, results concerning fixed points of contractive type mappings are found useful for determining the existence and uniqueness of solutions of various mathematical models
We refer the reader to the following references for surveys on these generalizations [1, 13,14,15,16,17,18]. One of these generalizations in the last decade is that of Azam et al [19, 20]. They introduced the notion of complex-valued metric spaces, and some fixed point theorems for mappings with some rational inequalities were
Inspired by [22], many authors have proven the existence of fixed points of different mappings satisfying rational inequalities in the framework of complex-valued b -metric spaces

Summary

Introduction

Fixed point theory is a well-researched area of mathematics; in particular, results concerning fixed points of contractive type mappings are found useful for determining the existence and uniqueness of solutions of various mathematical models. One of these generalizations in the last decade is that of Azam et al [19, 20] They introduced the notion of complex-valued metric spaces, and some fixed point theorems for mappings with some rational inequalities were. Inspired by [22], many authors have proven the existence of fixed points of different mappings satisfying rational inequalities in the framework of complex-valued b -metric spaces (see [19, 23] for more details). In 2016, Singh et al [24] introduced a contractive type mapping satisfying some rational inequalities They obtained the existence of common fixed point for a pair of singlevalued mappings satisfying more general contraction conditions in the framework of complex-valued metric spaces. Our result improves and strengthens the results of [20, 22, 28, 29] and many other related results in the literature

Preliminaries

Main Result

Application