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

Abstract

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.

Keywords

• common fixed point
• contraction conditions
• integral equations
• cone metric space