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A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces. (English) Zbl 1158.47317

Summary: We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S.Takahashi and W.Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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References:

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