DOI: 10.24193/fpt-ro.2023.1.17

Authors: Bancha Panyanak

Abstract: In this paper, we introduce the notion of generalized Berinde nonexpansive mappings in metric spaces and show that it is weaker than the notion of Berinde nonexpansive mappings and stronger than the notion of semi-nonexpansive mappings. We also obtain the semiclosed principle, an endpoint theorem, and a common endpoint theorem for generalized Berinde nonexpansive mappings. Strong and Δ-convergence theorems of the Ishikawa iteration process for semi-nonexpansive mappings are also discussed.

Key Words and Phrases: Endpoint, fixed point, generalized Berinde nonexpansive mapping, semi-nonexpansive mapping, uniformly convex hyperbolic space.

2010 Mathematics Subject Classification: 47H09, 47H10.

Published on-line: February 1st, 2023.

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