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

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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.

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Author information

Authors and Affiliations

  1. School of Education, Shan Dong Women’s University, Jinan, 056210, China

    Gaobo Li

  2. Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China

    Yanxia Lu

  3. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Yeol Je Cho

Authors
  1. Gaobo Li
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  2. Yanxia Lu
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  3. Yeol Je Cho
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Corresponding authors

Correspondence to Gaobo Li, Yanxia Lu or Yeol Je Cho.

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Li, G., Lu, Y. & Cho, Y.J. Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces. Indian J Pure Appl Math 50, 903–921 (2019). https://doi.org/10.1007/s13226-019-0363-2

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  • DOI: https://doi.org/10.1007/s13226-019-0363-2

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