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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    An Approximation Algorithm for the Combination of G-Variational Inequalities and Fixed Point Problems
    (2025-01-01)
    Kheawborisut, Araya
    ;
    Kangtunyakarn, Atid
    In this paper, we introduce a modified form of the G-variational inequality problem, called the combination of G-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed G-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the G-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the G-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings.
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    Modified subgradient extragradient method for system of variational inclusion problem and finite family of variational inequalities problem in real Hilbert space
    (2021-01-01)
    Kheawborisut, Araya
    ;
    Kangtunyakarn, Atid
    For the purpose of this article, we introduce a modified form of a generalized system of variational inclusions, called the generalized system of modified variational inclusion problems (GSMVIP). This problem reduces to the classical variational inclusion and variational inequalities problems. Motivated by several recent results related to the subgradient extragradient method, we propose a new subgradient extragradient method for finding a common element of the set of solutions of GSMVIP and the set of a finite family of variational inequalities problems. Under suitable assumptions, strong convergence theorems have been proved in the framework of a Hilbert space. In addition, some numerical results indicate that the proposed method is effective.
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    Algorithms of Common Solutions to Modified Generalized System of Variational Inclusion Problem and Hierarchical Fixed Point Problem
    (2022-01-01)
    Kheawborisut, Araya
    ;
    Kangtunyakarn, Atid
    This manuscript deals with two problems: the first one is a new problem of the system of variational inclusion that is called modified generalized system of variational inclusion problem(MGSVIP) and the other one is a hierarchical fixed point problem in the framework of real Hilbert space. We estab-lish the important lemma that show the relation between fixed point of nonlinear mapping and solution of MGSVIP for proving the main theorem. To approximate the common solution of these problems, we design an iterative scheme under suitable conditions on parameters. A strong convergence result for the proposed iterative scheme is proved. Applying our main result, we prove strong convergence theorems of the modification system of variational inequalities problem and variational inclusion problem. Moreover, we give the numerical example for supporting our results.
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    Approximating G-variational inequality problem by G-subgradient extragradient method in Hilbert space endowed with graphs
    (2023-01-01)
    Araveeporn, Autcha
    ;
    Kheawborisut, Araya
    ;
    Kangtunyakarn, Atid
    In this article, we introduce G-subgradient extragradient method for solving the G- variational inequality problem in Hilbert space endowed with a direct graph. Utilizing our mathematical tools, weak and strong convergence theorem are established for the proposed algorithm. In addition, we provide numerical experiments to illustrate the convergence behavior of our proposed algorithm.