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 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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    Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping
    (2023-01-01)
    Saechou, Kanyanee
    ;
    Kangtunyakarn, Atid
    The purpose of this research is to study the generalized modification of the system of equilibrium problems (GMSEP) and a lemma is established to show the property of this problem. Then, we prove a strong convergence theorem for finding a common element of the set of the solutions of the fixed points problem and the set of the solutions of the GMSEP under some suitable conditions, in which (Formula presented.), where (Formula presented.) are coefficients in the main iteration. Moreover, we prove strong convergence theorems for finding solutions to the generalized equilibrium problem, the system of equilibrium problems, the variational inequality problem, the general system of variational inequality problems, and the minimization problem. Finally, we give two numerical examples, one of which shows the rate of convergence of the main iteration while the other shows the rate of convergence of the main iteration but the sum of coefficients equals 1.
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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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    Convergence theorem for an intermixed iteration in p-uniformly convex metric space
    (2023-01-01)
    Saechou, Kanyanee
    ;
    Kangtunyakarn, Atid
    In this paper, we first introduce the intermixed algorithm in p-uniformly convex metric spaces, and then we prove Δ-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete p-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove Δ-convergence to solve the minimization problems in the framework of complete p-uniformly convex metric spaces. Finally, we give two examples in Lp spaces and numerical examples to support our main results.