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    A new approximation method for finding common elements of equilibrium problems, variational inequality problems and fixed point problems of nonspreading mappings
    (2017-10-01)
    Cheawchan, Kanyarat
    ;
    Phuengrattana, Withun
    ;
    In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of the equilibrium problem, the set of solutions of the variational inequality problem and the set of fixed points of a nonspreading mapping in Hilbert spaces. Under suitable assumptions, weak convergence theorems have been proved in the framework of a Hilbert space. Our results improve and extend the corresponding results existing in the current literature. In addition, a numerical result indicate that the proposed method is quite effective.
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    Item type:Publication,
    Approximation method for fixed points of nonlinear mapping and variational inequalities with application
    (2015-12-01)
    Cheawchan, Kanyarat
    ;
    In this paper, we introduce the new method of iterative scheme {x<inf>n</inf>} for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of a modified system of variational inequali- ties without demiclose condition and T<inf>ω</inf> := (1 − ω)I + ωT, when T is a quasi- nonexpansive mapping and ω ∈ (0, 1/2) in a framework of Hilbert space. Using our main result, we obtain strong convergence theorems involving a finite family of nonspreading mapping and another corollary.