A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems-Reference-Cited by-同舟云学术

A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems

Published:2023 Issue:5 Volume:8 Page:11037-11056
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Dechboon Premyuda¹,Adamu Abubakar²³⁴,Kumam Poom²⁵⁶

Affiliation:

1. Mathematics, Department of Learning Management, Faculty of Education, Burapha University, Chonburi Campus, 169 Long Haad Bangsaen Road, Saen Suk, Mueang, Chonburi 20131, Thailand

2. Center of Excellence in Theoretical and Computational Science, SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut's University of Technology Thonburi, 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

3. Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria

4. Operational Research Center in Healthcare, Near East University, Nicosia, TRNC, Turkey

5. KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $ q $-uniformly smooth real Banach spaces ($ q > 1 $). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $ l_4(\mathbb{R}) $ to study the effect of the relaxation and inertial parameters in our proposed algorithm.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference42 articles.

1. A. Adamu, D. Kitkuan, A. Padcharoen, C. E. Chidume, P. Kumam, Inertial viscosity-type iterative method for solving inclusion problems with applications, Math. Comput. Simulat., 194 (2022), 445–459. https://doi.org/10.1016/j.matcom.2021.12.007

2. A. Adamu, P. Kumam, D. Kitkuan, A. Padcharoen, Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications, Carpathian J. Math., 39 (2023), 1–26. https://doi.org/10.37193/CJM.2023.01.01

3. A. Adamu, J. Deepho, A. H. Ibrahim, A. B. Abubakar, Approximation of zeros of sum of monotone mappings with applications to variational inequality problem and image processing, Nonlinear Funct. Anal. Appl., 26 (2021), 411–432. https://doi.org/10.22771/NFAA.2021.26.02.12

4. A. Adamu, D. Kitkuan, P. Kumam, A. Padcharoen, T. Seangwattana, Approximation method for monotone inclusion problems in real Banach spaces with applications, J. Inequal. Appl., 2022 (2022), 70. https://doi.org/10.1186/s13660-022-02805-0

5. A. Adamu, A. A. Adam, Approximation of solutions of split equality fixed point problems with applications, Carpathian J. Math., 37 (2021), 381–392. https://doi.org/10.37193/CJM.2021.03.02

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