Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces

Gaobo Li (), Yanxia Lu () and Yeol Je Cho ()
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Gaobo Li: Shan Dong Women’s University
Yanxia Lu: North China Electric Power University
Yeol Je Cho: Gyeongsang National University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 4, 903-921

Abstract: Abstract In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two nonexpansive nonself-mappings is proved. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. Our result improves the ones of others in the literature.

Keywords: Nonexpansive mappings; equilibrium problems; Hilbert spaces (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0363-2

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