Iterative algorithms for solving the system of mixed equilibrium problems, fixed-point problems, and variational inclusions with application to minimization problem. (English) Zbl 1235.65062

Chamnarnpan, Tanom; Kumam, Poom

J. Appl. Math. 2012, Article ID 538912, 29 p. (2012).

Summary: We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a \(\beta\)-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

MSC:

65K05	Numerical mathematical programming methods
49J40	Variational inequalities
47H10	Fixed-point theorems

References:

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