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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    Modified Halpern Iteration for Finding a Common Element of the Set of Solutions of Generalized Equilibrium Problem and Fixed Point Problem of Quasi-nonexpansive Mapping
    (2025-09-01)
    Sripattanet, Anchalee
    ;
    Kangtunyakarn, Atid
    In this paper, we introduce an iterative process for finding a common element of the set of solutions of generlized equilibrium problem and the set of fixed points problem of a quasi-nonexpansive mapping without demi-closed condition and T<inf>ω</inf>:= (1 − ω)I + ωT, where T is a quasi-nonexpansive mapping and ω ∈ (0,<sup>1</sup>) in a framework of a real Hilbert space. By using our main result, we obtain 2 strong convergence theorems involving finite families of nonspreading mapping and κ-demicontractive mapping.
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    An Enhanced Subgradient Extragradient Method for Fixed Points of Quasi-Nonexpansive Mappings Without Demi-Closedness
    (2025-09-01)
    Sripattanet, Anchalee
    ;
    Kangtunyakarn, Atid
    This research focuses on developing a novel approach to finding fixed points of quasi-nonexpansive mappings without relying on the demi-closedness condition, a common requirement in previous studies. The approach is based on the Subgradient Extragradient technique, which builds upon the foundational extragradient method introduced by G.M. Korpelevich. Korpelevich’s method is a widely recognized tool in the fields of optimization and variational inequalities. This study extends Korpelevich’s technique by adapting it to a broader class of operators while maintaining critical convergence properties. This research demonstrates the effectiveness and practical applicability of this new method through detailed computational examples, highlighting its potential to address complex mathematical problems across various domains.
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    An Approximation Method for Solving Fixed Points of General System of Variational Inequalities with Convergence Theorem and Application
    (2021-01-01)
    Worapun, Phannipa
    ;
    Kangtunyakarn, Atid
    In this paper, we introduce an iterative scheme {x<inf>n</inf>} for finding a common element of the set of fixed points of quasi-nonexpansive mapping and the solution set of general system of variational inequality problems. We prove strong convergence theorem without condition T<inf>ω</inf> = (1 − ω)I + ωT, and demiclosed condition, where T is a quasi-nonexpansive mapping on Hilbert space. Strong convergence theorems are established in the framework of Hilbert spaces.
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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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    Convergence analysis for the equilibrium problems with numerical results
    (2014-12-22)
    Suwannaut, Sarawut
    ;
    Kangtunyakarn, Atid
    In this paper, we propose an iterative scheme modified from the work of Ceng et al. (Nonlinear Anal. Hybrid Syst. 4:743-754, 2010) and Plubtieng and Punpaeng (J. Math. Anal. Appl. 336(1):455-469, 2007) to prove the strong convergence theorem for approximating a common element of the set of fixed points of nonspreading mappings and a finite family of the set of solutions of the equilibrium problem. Using this result, we obtain the strong convergence theorem for a finite family of nonspreading mappings and a finite family of the set of solutions of equilibrium problem. Moreover, in order to compare numerical results between the combination of the equilibrium problem and the classical equilibrium problem, some examples are given in one- and two-dimensional spaces of real numbers.