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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 15
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Articles

Relaxed inertial Tseng extragradient method for variational inequality and fixed point problems

, , &
Pages 4253-4278 | Received 05 Oct 2021, Accepted 24 Jul 2022, Published online: 03 Aug 2022
 

Abstract

In this paper, we introduce a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. We prove a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Moreover, we apply our results to approximate solution of convex minimization problem, and we present some numerical experiments to show the efficiency and applicability of our method in comparison with some existing methods in the literature. Our proposed method is easy to implement. It requires only one projection onto a constructible half-space.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors sincerely thank the reviewers for their careful reading, constructive comments and useful suggestions. The opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF.

Disclosure statement

The authors declare that they have no competing interests.

Additional information

Funding

The research of the second author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers [grant number 119903].

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