DOI: 10.24193/fpt-ro.2024.1.10

Authors: A. Amini-Harandi, M. Goli and H.R. Hajisharifi

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.

Key Words and Phrases: Fixed point, Picard operator, (α,β)-nonexpansive mapping.

2010 Mathematics Subject Classification: 47H04, 47H10, 54H25.

Published on-line: February 1st, 2024.

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