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Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings. (English) Zbl 1151.65058

The authors introduce a new iterative scheme by the viscosity approximation method for finding a common element of the set of an equilibrium problem of the form
find \(u\in C\) such that \(\varphi(u, v)\geq 0\), \(\forall v\in C\), where \(\varphi\) is an bifunction of \(C\times C\) and \(C\) is a nonempty closed convex subset of a Hilbert space \(H\), and the set of fixed points of nonexpansive mappings in a Hilbert space \(H\).
Furthermore, a strong convergence theorem is proved which is an improvement and extension of the results of S. Takahashi and W. Takahashi [J. Math. Anal. Appl. 331, No. 1, 506–515 (2007; Zbl 1122.47056)].

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49J27 Existence theories for problems in abstract spaces

Citations:

Zbl 1122.47056
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References:

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