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Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings

Dinh, B.V. and Kim, D.S. (2017) Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings. Optimization Letters, 11 (3). pp. 537-553. ISSN 18624472

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Abstract

In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence of the iterates generated by each method is obtained under assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed at 0, and the bifunction associated with the equilibrium problem is weakly continuous. The bifunction is assumed to be satisfying a Lipschitz-type condition when the basic iteration comes from the extragradient method. It becomes unnecessary when an Armijo back tracking linesearch is incorporated in the extragradient method. © 2016, Springer-Verlag Berlin Heidelberg.

Item Type: Article
Divisions: Faculties > Faculty of Information Technology
Identification Number: 10.1007/s11590-016-1025-5
Uncontrolled Keywords: Algorithms; Mapping; Armijo linesearch; Equilibrium problem; Extragradient methods; Fixed-point problem; Monotonicity; Strong convergence; Iterative methods
Additional Information: Language of original document: English. All Open Access, Green.
URI: http://eprints.lqdtu.edu.vn/id/eprint/9735

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