Affiliation:
1. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa
Abstract
Abstract
In this paper, we introduce and study the concept of split monotone variational inclusion problem with multiple output sets (SMVIPMOS).
We propose a new iterative scheme, which employs the viscosity approximation technique for approximating the solution of the SMVIPMOS with fixed point constraints of a nonexpansive mapping in real Hilbert spaces.
The proposed method utilises the inertial technique for accelerating the speed of convergence and a self-adaptive step size so that its implementation does not require prior knowledge of the operator norm.
Under mild conditions, we obtain a strong convergence result for the proposed algorithm and obtain a consequent result, which complements several existing results in the literature.
Moreover, we apply our result to study the notions of split variational inequality problem with multiple output sets with fixed point constraints and split convex minimisation problem with multiple output sets with fixed point constraints in Hilbert spaces.
Finally, we present some numerical experiments to demonstrate the implementability of our proposed method.
Funder
National Research Foundation
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference58 articles.
1. R. P. Agarwal, D. O’Regan and D. R. Sahu,
Fixed Point Theory for Lipschitzian-Type Mappings with Applications,
Topol. Fixed Point Theory Appl. 6,
Springer, New York, 2009.
2. T. O. Alakoya, L. O. Jolaoso and O. T. Mewomo,
Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems,
Optimization 70 (2021), no. 3, 545–574.
3. T. O. Alakoya and O. T. Mewomo,
Viscosity 𝑆-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems,
Comput. Appl. Math. 41 (2022), no. 1, Paper No. 39.
4. T. O. Alakoya, A. O. E. Owolabi and O. T. Mewomo,
An inertial algorithm with a self-adaptive step size for a split equilibrium problem and a fixed point problem of an infinite family of strict pseudo-contractions,
J. Nonlinear Var. Anal. 5 (2021), 803–829.
5. T. O. Alakoya, A. Taiwo and O. T. Mewomo,
On system of split generalised mixed equilibrium and fixed point problems for multivalued mappings with no prior knowledge of operator norm,
Fixed Point Theory 23 (2022), no. 1, 45–74.
Cited by
17 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献