## 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

Zbl 1122.47056
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### References:

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