Inertial algorithm for solving split inclusion problem in Banach spaces

Ajay Kumar; Ekta Tamrakar

doi:10.56754/0719-0646.2501.067

DOI:

https://doi.org/10.56754/0719-0646.2501.067

Abstract

The purpose of this paper is to propose an algorithm for finding a common element of the set of fixed points of relatively nonexpansive mapping and the set of solutions of split inclusion problem with a way of selecting the stepsize without prior knowledge of the operator norm in the framework of Banach spaces. Then, the main result is used to the common fixed point problems of a family of relatively nonexpansive mappings and split equilibrium problem. Finally, a numerical example is provided to illustrate the main result.

Keywords

Strong convergence , split feasibility problem , uniformly convex , uniformly smooth , fixed point problem

Mathematics Subject Classification:

47H10 , 47J25 , 65J15

Ajay Kumar School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010 India. https://orcid.org/0000-0003-0550-2985
Ekta Tamrakar School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010 India. https://orcid.org/0000-0002-1183-3484

Pages: 67–88
Date Published: 2023-04-24
Vol. 25 No. 1 (2023)

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