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Mathematics 2019, 7(3), 270; https://doi.org/10.3390/math7030270

Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions

1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2
Center for General Education, China Medical University, Taichung 40402, Taiwan
3
Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
4
Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania
5
Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan
6
School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
7
The Key Laboratory of Intelligent Information and Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China
*
Author to whom correspondence should be addressed.
Received: 18 February 2019 / Revised: 10 March 2019 / Accepted: 13 March 2019 / Published: 16 March 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Full-Text   |   PDF [337 KB, uploaded 25 March 2019]

Abstract

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions. View Full-Text
Keywords: extragradient-like method; minimization problem; variational inclusion; generalized mixed equilibrium problem extragradient-like method; minimization problem; variational inclusion; generalized mixed equilibrium problem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ceng, L.-C.; Postolache, M.; Wen, C.-F.; Yao, Y. Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions. Mathematics 2019, 7, 270.

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