(α, β)-NONEXPANSIVE MAPPINGS AND PICARD OPERATORS

Abstract

Let C be a nonempty closed bounded (not necessary convex) subset of a Banach space X and let T: C → C be an (α, β)-nonexpansive mapping with α > 0, β > 0 and α + β < 1. In this paper, we show that T has a unique fixed point. Moreover, T is a Picard operator if and only if T is asymptotically regular. © 2024, House of the Book of Science. All rights reserved.