Common Fixed Point Theorems Of Weakly Compatible Maps Satisfying (f,g)-Weakly Contractive Condition And Invariant Approximation Results

Abstract

We prove the existence of common fixed points for three selfmaps $T,f$ and $g$ defined on a metric space $(X,d)$ satisfying, $T$ is $(f,g)$-weakly contractive; and the pairs $(T,f)$ and $(T,g)$ are weakly compatible. Also, for such $T,f$ and $g$, we prove the convergence of modified Mann iteration and modified Ishikawa iteration with respect to $T,f$ and $g$ to their common fixed point, in a normed space. Further, we obtain invariant approximation results from the set of best approximations to common fixed points of $T,f$ and $g$.