Invariant Approximation Results via Common Fixed Point Theorems for Generalized Weak Contraction Maps

Abstract

A common fixed point theorem for generalized ${\left(\phi ,\varphi ,L \right)}_{f,g}$-weak contraction in a metric space is established. As an application, some common fixed point results in normed linear spaces are obtained. We also study some results on best approximation via common fixed point theorems. Our result improves some results from the existing literature. Some illustrative examples to highlight the realized improvements are also furnished.