CONVERGENCE AND STABILITY OF PICARD S-ITERATION PROCEDURE FOR CONTRACTIVE-LIKE OPERATORS

Abstract

Let $(X,\Vert .\Vert )$ be a normed linear space. Let $K$ be a nonempty closed convex subset of $X$. Let $T:K\to K$ be a contractive-like operator with a nonempty fixed point set $F(T)$. We prove the strong convergence and $T$-stability of Picard S-iteration procedure with respect to the contractive-like operator $T$ which are independent for any arbitrary choices of the sequences $\{{\alpha }_n{\}}_{n=0}^{\mathrm{\infty }}$ and $\{{\beta }_n{\}}_{n=0}^{\mathrm{\infty }}$ in $[0,1]$.