Common fixed points and convergence results for α-Krasnosel'skii mappings

Abstract

We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with α-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.

Keywords

• α-krasnosel'skii iteration
• approximation
• asymptotically regular
• iterative methods
• metric projection
• schauder theorem
• uniformly convex banach space