TY - JOUR
T1 - A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods
AU - Jolaoso, Lateef Olakunle
AU - Taiwo, Adeolu
AU - Alakoya, Timilehin Opeyemi
AU - Mewomo, Oluwatosin Temitope
N1 - Funding Information:
The authors sincerely thank the Editor in Chief and the anonymous reviewers for their careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The first author acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) (BA2019-039) Doctoral Bursary. The second author acknowledges with thanks the International Mathematical Union Breakout Graduate Fellowship (IMU-BGF-20191101) Award for his doctoral study. The fourth 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, NRF and IMU.
Funding Information:
The authors sincerely thank the Editor in Chief and the anonymous reviewers for their careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The first author acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) (BA2019-039) Doctoral Bursary. The second author acknowledges with thanks the International Mathematical Union Breakout Graduate Fellowship (IMU-BGF-20191101) Award for his doctoral study. The fourth 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, NRF and IMU.
Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.
AB - Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.
KW - Banach space
KW - Extragradient method
KW - Fixed point problem
KW - Iterative method
KW - Projection method
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85084504345&partnerID=8YFLogxK
U2 - 10.1007/s10957-020-01672-3
DO - 10.1007/s10957-020-01672-3
M3 - Article
AN - SCOPUS:85084504345
SN - 0022-3239
VL - 185
SP - 744
EP - 766
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -