Fixed points of relaxed $(\psi,\varphi)$-weakly $N$-contraction mappings in modular spaces

Abstract

The purpose of this paper is to study the existence and approximation of a common fixed point of a pair of mappings satisfying a relaxed $(\psi,\varphi)$-weakly $N$-contractive condition and
existence and approximation of a fixed point of a
relaxed $(\psi,\varphi)$-weakly $N$-contraction mapping
in the setting of modular spaces. Our theorems improve and generalize the results in Mongkolkeha and Kumam \cite{MON1} and \"{O}zt\"{u}rk et. al \cite{OZT1}. To validate our results numerical examples are provided.