Kangtunyakarn, Atid

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Kangtunyakarn, Atid
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Kangtunyakarn, A.
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atid.ka@kmitl.ac.th

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    Convergence theorem of common fixed points for a family of nonspreading mappings in Hilbert space
    (2012-06-01)
    Kangtunyakarn, Atid
    We introduce the concept of K-mapping of a finite family of nonspreading mappings {T <inf>i</inf>} <sup>N</sup> <inf>i=1</inf> and we show that the fixed point set of the K-mapping is the set of common fixed points of {T <inf>i</inf>} <sup>N</sup> <inf>i=1</inf>. Moreover, we prove strong convergence theorem of the Ishikawa iterative process to a common fixed point of a finite family of nonspreading mappings in Hilbert space under certain control conditions. © 2011 Springer-Verlag.
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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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    Strong convergence theorem for the split equality fixed point problem for quasi-nonexpansive mapping and application
    (2019-01-01)
    Premjitpraphan, S.
    ;
    Kangtunyakarn, A.
    Motivated by the work of Zhao [9], [10], [11] and by reducing some of his conditions, we consider a split equality fixed point problem for quasi-nonexpansive mappings which includes split feasibility problem, split equality problem, split fixed point problem, etc. The strong convergence theorem of the proposed iterative scheme could be obtained, under some control conditions. Furthermore, we use S-mapping applied to our main result to prove strong convergence theorems.
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    Strong convergence of the hybrid method for a finite family of nonspreading mappings and variational inequality problems
    (2012-01-01)
    Kangtunyakarn, Atid
    In this paper, we prove a strong convergence theorem by the hybrid method for finding a common element of the set of fixed points of a finite family of nonspreading mappings and the set of solutions of a finite family of variational inequality problems. © 2012 Kangtunyakarn; licensee Springer.
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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.