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Open AccessArticle

Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators

1
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
2
The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China
3
Department of Mathematics, King Abdulaziz University, P. O. B. 80203, Jeddah 21589, Saudi Arabia
4
Center for General Education, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 461; https://doi.org/10.3390/math8040461
Received: 12 December 2019 / Revised: 13 March 2020 / Accepted: 19 March 2020 / Published: 25 March 2020
The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractive operators and the pseudomonotone equilibrium problem in Hilbert spaces. The suggested iterative algorithm is based on the projected method and subgradient method with a linearsearch technique. We show the strong convergence result for the iterative sequence generated by this algorithm. Some applications are also included. Our result improves and extends some existing results in the literature. View Full-Text
Keywords: equilibrium problem; pseudomonotone; fixed point; pseudocontractive operators; subgradient equilibrium problem; pseudomonotone; fixed point; pseudocontractive operators; subgradient
MDPI and ACS Style

Yao, Y.; Shahzad, N.; Yao, J.-C. Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators. Mathematics 2020, 8, 461.

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