Work

Ergodic theory for monotone Reich–Suzuki type nonexpansive operators

Year: 2025

Type: article

Abstract: A recent study on nonexpansive monotone operators on partially ordered Banach spaces revealed that the sequence of Cesàro means converges to a fixed point, but also plays an instrumental role in the convergence analysis of the Picard successive approximations. Throughout this paper we provide a new iterative construction of Krasnoselskii type, as alternative to the ergodic iteration, that also supports the analysis of the Picard iterative sequence. Moreover, this study considers a wider class of monotone nonexpansive mappings, namely Reich–Suzuki type nonexpansive operators. Finally, a numerical simulation is provided by polynomiographic methods, so as to confirm the intuitive conclusions about the higher efficiency of the Picard iteration and the Krasnoselskii iteration compared to the ergodic procedure.

Source: Journal of Fixed Point Theory and Applications

DOI: 10.1007/s11784-025-01167-6

Authors: Andreea Bejenaru, Mihai Postolache

Institutions: Universitatea Națională de Știință și Tehnologie Politehnica București, North Minzu University, Romanian Academy

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W4407407291