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A new hybrid method for equilibrium problems, variational inequality problems, fixed point problems, and zero of maximal monotone operators. (English) Zbl 1235.65070

Summary: We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of L.-C. Zeng [Fixed Point Theory Appl. 2010, Article ID 590278, 33 p. (2010; Zbl 1207.47077)] and many others.

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems

Citations:

Zbl 1207.47077
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References:

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