A modified iterative Method for Solving Split variational Inclusion Problems and Fixed Point Problems for Nonexpansive Semigroup

  • F. O. Nwawuru Department of Mathematics, Faculty of Physical Sciences, Chukwuemeka Odumegwu Ojukwu University, Uli Campus, Anambra State.
  • B. E. Chukwuemeka Department of Mathematics, Faculty of Physical Sciences, Chukwuemeka Odumegwu Ojukwu University, Uli Campus, Anambra State.
DOI: https://doi.org/10.6084/m9.figshare.22347139
Keywords: Split variational inclusion problem, Inertial method, Fixed point problem, Hilbert spaces

Abstract

In this paper, we introduce and study a modified iterative method for approximating a common
solution of split variational inclusion problems and fixed point problems for nonexpansive
semigroup in real Hilbert spaces. We prove that the proposed method converges strongly to the
solution of the mentioned problem under some mild assuptions. A new inertial extrapolation
is introduced which is known to speed up the rate of covergence of iterative algorithms. Our
method uses self-adaptive stepsize that is generated at each iteration and does not depend norm
of the bounded linear operator which is difficult in practice. We give numerical illustrations
of the proposed scheme in comparison with other existing methods in the literature to further
justify the applicability and efficiency of our proposed algorithm.

Published
2023-03-29
How to Cite
Nwawuru, F. O., & Chukwuemeka, B. E. (2023). A modified iterative Method for Solving Split variational Inclusion Problems and Fixed Point Problems for Nonexpansive Semigroup. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(2), 109 - 130. https://doi.org/10.6084/m9.figshare.22347139
Issue
Vol 8 No 2 (2022)
Section
Articles

Copyright (c) 2023 F. O. Nwawuru, B. E. Chukwuemeka

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.