TY - JOUR
T1 - Inertial Mann-Krasnoselskii Algorithm with Self Adaptive Stepsize for Split Variational Inclusion Problem and Paramonotone Equilibria
AU - Jolaoso, Lateef O.
AU - Mebawondu, Akindele A.
AU - Mewomo, Oluwatosin T.
N1 - Funding Information:
The authors sincerely thank the reviewer for his careful reading, constructive comments and fruitful suggestions that improved the manuscript. The first and second author acknowledge with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF.
Publisher Copyright:
© 2022 The Author(s).
PY - 2022/4/27
Y1 - 2022/4/27
N2 - . In this paper, we introduce a Mann-Krasnoselskii algorithm of inertial form for approximating a common solution of Spit Variational Inclusion Problem (SVIP) and Equilibrium Problem (EP) with paramonotone bifunction in real Hilbert spaces. Motivated by the self-adaptive technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumptions such as monotonicity and lower semicontinuity of the SVIP and EP associated mappings, we establish the strong convergence of the iterative algorithm. Some applications and numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature. Our results improve and generalize many existing results in this direction.
AB - . In this paper, we introduce a Mann-Krasnoselskii algorithm of inertial form for approximating a common solution of Spit Variational Inclusion Problem (SVIP) and Equilibrium Problem (EP) with paramonotone bifunction in real Hilbert spaces. Motivated by the self-adaptive technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumptions such as monotonicity and lower semicontinuity of the SVIP and EP associated mappings, we establish the strong convergence of the iterative algorithm. Some applications and numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature. Our results improve and generalize many existing results in this direction.
KW - equilibrium problem
KW - pseudomonotonicity
KW - self adaptive stepsize
KW - split variational inclusion
UR - http://www.scopus.com/inward/record.url?scp=85130637099&partnerID=8YFLogxK
U2 - 10.3846/mma.2022.13949
DO - 10.3846/mma.2022.13949
M3 - Article
AN - SCOPUS:85130637099
SN - 1392-6292
VL - 27
SP - 179
EP - 198
JO - Mathematical Modelling and Analysis
JF - Mathematical Modelling and Analysis
IS - 2
ER -