SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.-Reference-Cited by-同舟云学术

SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.

Published:2023 Issue:1-2 Volume:15 Page:535-553
ISSN:2066-5997
Container-title:Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application
language:
Short-container-title:AnnalsARSciMath

Author:

Abass H. A., ,

Abstract

In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which includes the multiple-sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.

Publisher

Academia Oamenilor de Stiinta din Romania

Subject

General Mathematics

Reference29 articles.

1. [1] H. A. Abass, C. Izuchukwu, O. T. Mewomo, Q. L. Dong, Strong convergence of an inertial forward-backward splitting method for accretive operators in real Banach space, Fixed Point Theory, 20, no. 2, (2020), 397-412.

2. [2] H. A. Abass and L. O. Jolaoso, An inertial generalized viscosity approximation method for solving multiple-sets split feasibility problems and common fixed point of strictly pseudo-nonspreading mappings, Axioms, 10, no. 1, (2021),1.

3. [3] H.A. Abass, C.C. Okeke and O.T. Mewomo, On split equality mixed equilibrium and fixed point problems of generalized ki-strictly pseudo- contractive multi-valued mappings, Dyn. Contin. Discrete Impuls. Syst., Series B: Applications and Algorithms, 25, no. 6, (2018), 369395.

4. [4] H. A. Abass, K. O. Aremu, L. O. Jolaoso and O.T. Mewomo, An inertial forward-backward splitting method for approximating solutions of certain optimization problem, J. Nonlinear Funct. Anal. 2020, (2020), Article ID 6.

5. [5] F. Akutsah, O. K. Narain, H. A. Abass and A. A. Mebawondu, Shrinking approximation method for solution of split monotone variational inclusion and fixed point problems in Banach spaces, International J. Nonlinear Anal. Appl., 12, no. 2, (2021), 825-842.