Stability of Some Iteration Schemes in Cone Banach Spaces

Dipankar Das, Nilakshi Goswami

Abstract

In this paper, we discuss some stability theorems for mappings in cone Banach Spaces. Let $X$ be a cone Banach space with  normal cone $P$ and  $T$ be a self mapping on $X$ satisfying some specific condition. Here we derive different conditions under which the Mann iteration and Picard-Mann hybrid iteration schemes are stable in cone Banach space $X$. The stability of another iteration process converging to a common fixed point of two self mappings $S$ and $T$ on $X$ is also discussed here.