A generalized nonlinear iterative algorithm for the explicit midpoint rule of nonexpansive semigroup

Year 2020, Volume: 69 Issue: 1, 613 - 628, 30.06.2020

Hamid Reza Sahebi , Mahdi Azhını Masume Cheraghi

https://doi.org/10.31801/cfsuasmas.484452

Abstract

In this paper, we introduce a new iterative midpoint rule for finding a solution of xed point problem for a nonexpansive semigroup in real Hilbert spaces. We establish a strong convergence theorem for the sequences generated by our proposed iterative scheme. Furthermore, we provide application to Fredholm integral equations. A
numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.

Keywords

Nonexpansive semigroup, equilibrium problem, midpoint method, strongly positive linear bounded operator

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