Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems. (English) Zbl 1524.90245
Summary: 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 Hölder continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands
MSC:
| 90C25 | Convex programming |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 65K10 | Numerical optimization and variational techniques |
Keywords:
common fixed point problem; equilibrium problem; Hölder continuity; extragradient method; shrinking projectionReferences:
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