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

Authors : Hamid Reza SAHEBİ, Mahdi AZHINI, Masume CHERAGHİ

Pages : 613-628

Doi:10.31801/cfsuasmas.484452

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Publication Date : 2020-06-30

Article Type : Research Paper

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