%0 Journal Article %T Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems %J Computational Methods for Differential Equations %I University of Tabriz %Z 2345-3982 %A Bedane, Dejene Shewakena %A Gebrie, Anteneh Getachew %D 2022 %\ 07/01/2022 %V 10 %N 3 %P 639-655 %! Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems %K Common fixed point problem %K Equilibrium problem %K H¨older continuity %K Extragradient method %K Shrinking projection %R 10.22034/cmde.2021.44502.1879 %X 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 %U https://cmde.tabrizu.ac.ir/article_13350_b0780822f1440699cff665f59754d6e8.pdf