Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

Abstract EN

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation.

As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings.

Our results improve and extend a host of previously known results.

Moreover, we study the existence of solutions of a nonlinear integral equation.