Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems

Document Type : Research Paper


Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, P.O. Box 445, Ethiopia.


Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradient-like method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of a nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of the finite number of H ̈older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands


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