TY - JOUR
T1 - An extragradient algorithm for split generalized equilibrium problem and the set of fixed points of quasi-ϕ-nonexpansive mappings in Banach spaces
AU - Oyewole, Olawale Kazeem
AU - Mewomo, Oluwatosin Temitope
AU - Jolaoso, Lateef Olakunle
AU - Khan, Safeer Hussain
N1 - Funding Information:
The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments, and fruitful suggestions that improved the manuscript. The authors Oyewole and Jolaoso 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 author Mewomo 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:
© TUBITAK.
PY - 2020
Y1 - 2020
N2 - In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-ϕ-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex, and reflexive Banach space E2. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm in comparison with other existing algorithms in the literature. Our results extend and improve many recent results in this direction.
AB - In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-ϕ-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex, and reflexive Banach space E2. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm in comparison with other existing algorithms in the literature. Our results extend and improve many recent results in this direction.
KW - Banach space
KW - Linesearch rule
KW - Monotone mapping
KW - Quasi-phi-nonexpansive mapping
KW - Split generalized mixed equilibrium problem
KW - Strong convergence
UR - http://www.scopus.com/inward/record.url?scp=85089379604&partnerID=8YFLogxK
U2 - 10.3906/MAT-1911-83
DO - 10.3906/MAT-1911-83
M3 - Article
AN - SCOPUS:85089379604
VL - 44
SP - 1146
EP - 1170
JO - Turkish Journal of Mathematics
JF - Turkish Journal of Mathematics
SN - 1300-0098
IS - 4
ER -