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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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