University of TabrizComputational Methods for Differential Equations2345-398210320220701Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems6396551335010.22034/cmde.2021.44502.1879ENDejene ShewakenaBedaneDepartment of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, P.O. Box 445, Ethiopia.Anteneh GetachewGebrieDepartment of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, P.O. Box 445, Ethiopia.0000-0001-7368-8713Journal Article20210211<span dir="ltr" role="presentation">Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the </span><span dir="ltr" role="presentation">first algorithm is obtained using sequential computation of extragradient-like method and the second algorithm </span><span dir="ltr" role="presentation">is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed </span><span dir="ltr" role="presentation">points of a nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum </span><span dir="ltr" role="presentation">of the finite number of H ̈</span><span dir="ltr" role="presentation">older continuous bifunctions. The convergence theorems for iterative sequences generated </span><span dir="ltr" role="presentation">by the algorithms are established under widely used assumptions for the bifunction and its summands</span>https://cmde.tabrizu.ac.ir/article_13350_b0780822f1440699cff665f59754d6e8.pdf