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 intermixed algorithm for solving fixed point problems of proximal operators in Hilbert Spaces
    (2024-01-01)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    The aim of this paper is to modify proximal operators in Hilbert spaces. We introduce an inter-mixed algorithm with viscosity technique to find the solution of fixed point problem of two proximal operators in a real Hilbert space, utilizing the modified proximal operators. Under some mild conditions, a strong convergence theorem is established for the proposed algorithm. We also apply our main result to the split feasibility problem. Finally we provide numerical examples for supporting the main result.
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    The modification of generalized mixed equilibrium problems for convergence theorem of variational inequality problems and fixed point problems
    (2021-03-01)
    Khuangsatung, Wongvisarut
    ;
    Suantai, Suthep
    ;
    Kangtunyakarn, Atid
    The purpose of this research, we modify generalized mixed equilibrium problems and prove a strong convergence theorem for approximating a common element of the set of such a problem and variational inequality problems and the set of fixed points of infinite family of strictly pseudo contractive mappings. Utilizing our main result, we also prove a strong convergence theorem involving generalized equilibrium problems and variational inequality problems.
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    An intermixed method for solving the combination of mixed variational inequality problems and fixed-point problems
    (2023-01-01)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    In this paper, we introduce an intermixed algorithm with viscosity technique for finding a common solution of the combination of mixed variational inequality problems and the fixed-point problem of a nonexpansive mapping in a real Hilbert space. Moreover, we propose the mathematical tools related to the combination of mixed variational inequality problems in the second section of this paper. Utilizing our mathematical tools, a strong convergence theorem is established for the proposed algorithm. Furthermore, we establish additional conclusions concerning the split-feasibility problem and the constrained convex-minimization problem utilizing our main result. Finally, we provide numerical experiments to illustrate the convergence behavior of our proposed algorithm.
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    A method for solving the variational inequality problem and fixed point problems in Banach spaces
    (2021-04-14)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.
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    Strong Convergence for the Modified Split Monotone Variational Inclusion and Fixed Point Problem
    (2022-06-01)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    The purpose of this research is to modify the split monotone variational inclusion problem and prove a strong convergence theorem for finding a common element of the set of solutions of this problem and the set of fixed points of a nonexpansive mapping in Hilbert space. We also apply our main result involving a κ-strictly pseudo-contractive mapping. Moreover, we give the numerical example to support some of our results.
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    The Method for Solving Fixed Point Problem of G-Nonexpansive Mapping in Hilbert Spaces Endowed with Graphs and Numerical Example
    (2020-03-01)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    The main aim of this paper is to study a strong convergence theorem of viscosity approximation method for G-nonexpansive mapping defined on a Hilbert space endowed with a directed graph. By using our main result, we give a numerical expample to approximate the value of π.
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    A novel iterative algorithm for solving a class of variational inequality problems: revisions to ‘On the intermixed method for mixed variational inequality problems: another look and some corrections’
    (2025-12-01)
    Khuangsatung, Wongvisarut
    ;
    Kangtunyakarn, Atid
    In this paper, we investigate the combination of mixed variational inequality problems and propose a novel algorithm that integrates the subgradient extragradient method with the Krasnoselskii-Mann-type method. This algorithm aims to find a common solution for the combination of mixed variational inequality problems and two sets of variational inequality problems in a real Hilbert space. Importantly, our work addresses and corrects certain errors in Saejung’s study (J. Inequal. Appl. 2024:42, 2024) concerning mixed variational inequality problems, which were initially introduced in Khuangsatung and Kangtunyakarn’s research (J. Inequal. Appl. 2023:1, 2023). We establish the weak and strong convergence result for the proposed algorithm under suitable conditions. As an application, we apply our main results to the split feasibility problem and the constrained convex minimization problem. Finally, a numerical example is provided to demonstrate the convergence behavior of the algorithm.
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    A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs
    (2024-01-01)
    Khuangsatung, Wongvisarut
    ;
    Singta, Akarate
    ;
    Kangtunyakarn, Atid
    This article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.