Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space

Abstract

Let $(X, d)$ be a cone metric space and $T : X → X$ be a mapping. In this paper, we shall introduce the concept of strong $T$-stability of fixed point iteration procedures with respect to $T$ in cone metric spaces. Also, we will investigate some meaningful results on strong $T$-stability of Picard iterations in cone metric spaces without the assumption of normality. Our main results improve and generalize some related results in the literature.