A novel approach of multi-valued contraction results on cone metric spaces with an application

Abstract

<abstract><p>In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations.</p></abstract>

The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation

“…In this regard, by modifying the triangle inequality, Vulpe et al [23] were the first to propose a generalized form of a metric space (b-metric space) in 1981 due to Berinde and Pȃcurar [6] according to the current bibliographical knowledge. In the same direction, Hussain and Shah [10] generalized the notion of a b-metric space by changing the set of real numbers by an ordered Banach space, and they proved some fixed point theorems on this type of spaces called the cone b-metric space, which is also a generalization of the idea of a cone metric space [2,11,14,21].…”