TY - JOUR
T1 - Fast and Simple Bregman Projection Methods for Solving Variational Inequalities and Related Problems in Banach Spaces
AU - Gibali, Aviv
AU - Jolaoso, Lateef Olakunle
AU - Mewomo, Oluwatosin Temitope
AU - Taiwo, Adeolu
N1 - Funding Information:
The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges 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). The fourth author acknowledges with thanks the International Mathematical Union (IMU) Breakout Graduate Fellowship Award for his doctoral study. 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 anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges 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). The fourth author acknowledges with thanks the International Mathematical Union (IMU) Breakout Graduate Fellowship Award for his doctoral study. 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 Nature Switzerland AG.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - In this paper, we study the problem of finding a common solution to variational inequality and fixed point problems for a countable family of Bregman weak relatively nonexpansive mappings in real reflexive Banach spaces. Two inertial-type algorithms with adaptive step size rules for solving the problem are presented and their strong convergence theorems are established. The usage of the Bregman distances and the Armijo line search technique (which avoids the need to know a priori the Lipschitz constant of the involved operators), enable great flexibility of the proposed scheme, and besides their theoretical extensions, it might also have a practical potential.
AB - In this paper, we study the problem of finding a common solution to variational inequality and fixed point problems for a countable family of Bregman weak relatively nonexpansive mappings in real reflexive Banach spaces. Two inertial-type algorithms with adaptive step size rules for solving the problem are presented and their strong convergence theorems are established. The usage of the Bregman distances and the Armijo line search technique (which avoids the need to know a priori the Lipschitz constant of the involved operators), enable great flexibility of the proposed scheme, and besides their theoretical extensions, it might also have a practical potential.
KW - Banach spaces
KW - Bregman weak relatively nonexpansive mappings
KW - Variational inequality problem
KW - inertial-type algorithm
UR - http://www.scopus.com/inward/record.url?scp=85094672889&partnerID=8YFLogxK
U2 - 10.1007/s00025-020-01306-0
DO - 10.1007/s00025-020-01306-0
M3 - Article
AN - SCOPUS:85094672889
SN - 1422-6383
VL - 75
JO - Results in Mathematics
JF - Results in Mathematics
IS - 4
M1 - 179
ER -