Title of article :
Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems
Author/Authors :
Shewakena Bedane, Dejene Department of Mathematics - College of Computational and Natural Science - Debre Berhan University - Debre Berhan ,Ethiopia , Getachew Gebrie, Anteneh Department of Mathematics - College of Computational and Natural Science - Debre Berhan University - Debre Berhan ,Ethiopia
Abstract :
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
Keywords :
Common fixed point problem , Equilibrium problem , H¨older continuity , Extragradient method , Shrinking projection
Journal title :
Computational Methods for Differential Equations
