Kangtunyakarn, Atid

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Kangtunyakarn, Atid
Alternative Name
Kangtunyakarn, A.
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Email
atid.ka@kmitl.ac.th

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    The modified split generalized equilibrium problem for quasi-nonexpansive mappings and applications
    (2018-01-01)
    Cheawchan, Kanyarat
    ;
    Kangtunyakarn, Atid
    In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme { x<inf>n</inf>} for finding a common element of the set of solutions of variational inequality problems and the set of common fixed points of a finite family of quasi-nonexpansive mappings and the set of solutions of the modified split generalized equilibrium problem without assuming a demicloseness condition and T<inf>ω</inf>: = (1 − ω) I+ ωT, where T is a quasi-nonexpansive mapping and ω∈(0,12); a difficult proof in the framework of Hilbert space. In addition, we give a numerical example to support our main result.
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    A new technique for convergence theorem of fixed point problem of quasi-nonexpansive mapping
    (2015-12-01)
    Cheawchan, Kanyarat
    ;
    Suantai, Suthep
    ;
    Kangtunyakarn, Atid
    For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified system of variational inequalities without demiclosed condition of W and W<inf>ω</inf>:=(1−ω)I+ωW, where W is a quasi-nonexpansive mapping and (Formula presented.) in the framework of Hilbert space. By using our main result, we obtain a strong convergence theorem involving a finite family of nonspreading mappings and another corollary. Moreover, we give a numerical example to encourage our main theorem.
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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
    ;
    Kangtunyakarn, Atid
    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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    Approximation method for fixed points of nonlinear mapping and variational inequalities with application
    (2015-12-01)
    Cheawchan, Kanyarat
    ;
    Kangtunyakarn, Atid
    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.
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    Modified Halpern’s iteration without assumptions on fixed point set in metric space
    (2019-01-01)
    Cheawchan, Kanyarat
    ;
    Kangtunyakarn, Atid
    By improving Halpern’s iteration and studing convergence theorem of [1] and [2] in a complete uniformly convex metric space, we prove convergence theorem of a finite family of nonexpansive mappings without the assumption that “the set of common fixed points of nonexpansive mappings is nonempty”. We also introduce a mapping in metric space using a concept of the S-mapping defined by [3] for proving our main results.