Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007)

A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

[EN] The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.Izuchukwu, C.; Aremu, KO.; Mebawondu, AA.; Mewomo, OT. (2019). A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space. Applied General Topology. 20(1):193-210. https://doi.org/10.4995/agt.2019.10635SWORD193210201K. O. Aremu, C. Izuchukwu, G. C. Ugwunnadi and O. T. Mewomo, On the proximal point algorithm and demimetric mappings in CAT(0) spaces, Demonstr. Math. 51 (2018), 277-294. https://doi.org/10.1515/dema-2018-0022M. 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Parallel extragradient-proximal methods for split equilibrium problems

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the hybrid (outer approximation) method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions.Comment: 13 pages, submitte