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ABSTRACT
In this paper, we propose a new viscosity type inertial extragradient method with Armijo line-search technique for approximating a common solution of equilibrium problem with pseudo-monotone bifunction and fixed points of relatively nonexpansive mapping in a real Hilbert space. Two advantages of our algorithm are that its convergence does not require the bifunction to satisfy any Lipschitz-type condition and only one strongly convex program and one projection onto the feasible set are perform at each iteration. Under some mild conditions on the control sequences, we state and prove a strong convergence theorem and also present two numerical examples to illustrate the performance of our algorithm. The results in this paper improve and generalize many recent results in this direction in the literature.
Acknowledgments
The authors sincerely thank 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 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 acknowledges with thanks the International Mathematical Union Breakout Graduate Fellowship (IMU-BGF) 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, IMU and NRF.
Disclosure statement
No potential conflict of interest was reported by the authors.