Kangtunyakarn, Atid

Preferred name

Kangtunyakarn, Atid

Alternative Name

Kangtunyakarn, A.

Main Affiliation

School of Science

atid.ka@kmitl.ac.th

Now showing 1 - 9 of 9

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Modified intermixed iteration for solving the split general system of variational inequality problems and applications
(2021-12-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
Inspired by the works of Siriyan and Kangtunyakarn (2018) and Yao et al. (2015), we first introduce the two-step intermixed iteration for finding a common element of the set of the solutions of the split general system of variational inequality problem (SGSV), and also, we prove strong convergence theorem of the intermixed algorithm. Using our main theorem, we prove strong convergence theorems for finding solutions to the split variational inequality problem (SVIP), the split feasibility problem (SFP), and the split common fixed point problem (SCFP). Moreover, we give three numerical examples of these classical problems introduced by the previous studies and an example that conflicts with our main theorem where some conditions fail.
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A three-intermixed algorithm for common fixed point problems with applications to convex optimization and network allocation
(2026-07-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
This study investigates a new algorithm, termed the three-intermixed algorithm, developed from the intermixed algorithm introduced by Yao et al. (Fixed Point Theory Appl 206, 2015). A strong convergence theorem is established for finding a common element in the set of fixed points of nonexpansive mappings. To illustrate our main theorem, we provide an example in R2 along with a graphical representation showing the behavior of the sequences {xn},{yn}, and {zn}. Beyond theoretical development, the applicability of the main theorem is demonstrated through several important problems, including the convex minimization problem, the split feasibility problem, and both general and new systems of variational inequality problems. In addition, a special case of the main theorem is applied to the network bandwidth allocation problem. A detailed numerical example is presented to show how the proposed iterative scheme can be used to compute a proportionally fair allocation under capacity and minimum rate constraints, thereby confirming the practical efficiency of the method.
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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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An intermixed iteration for constrained convex minimization problem and split feasibility problem
(2019-01-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.
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The subgradient extragradient method for approximation of fixed-point problem and modification of equilibrium problem
(2023-01-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
In this paper, we consider the modification of equilibrium problem (MEP) and new subgradient extragradient algorithm by using the concept of the set of solutions of the modified variational inequality problem introduced by [Kangtunyakarn A. A new iterative scheme for fixed-point problems of infinite family of (Formula presented.) pseudo contractive mappings, equilibrium problem, variational inequality problems. J Optim Theory Appl. 2013;56:1543–1562.]. Then, we establish and prove weak and strong convergence theorem of the new subgradient extragradient algorithm for finding a common element of the set of solutions of the MEP and two sets of the variational inequality problems under some suitable conditions on (Formula presented.) and (Formula presented.) with (Formula presented.). Moreover, we apply our main theorem to prove weak and strong convergence theorems to solve the generalized equilibrium problem, the system of equilibrium problem, the variational inequality problem and the general system of variational inequality problems. Finally, we give two numerical examples to support our main result.
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The approximate solution of the general split variational inequality problem by intermixed iteration
(2025-01-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
This paper first introduces a new problem that is the general split variational inequality problem and invents a mathematical tool for solving our new problem which is Lemma 2.5. Then, we establish and prove a strong convergence theorem aimed at finding an element of the set of the solution of the general split variational inequality problem. Furthermore, we apply our main theorem to demonstrate a strong convergence theorem for finding solutions to the split variational inequality problem, the split feasibility problem, and the minimization problem. Finally, we provide numerical examples to advocate our main result.
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The method for solving the extension of general of the split feasibility problem and fixed point problem of the cutter
(2022-01-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
This paper first introduces a new iterative method for weak and strong convergence theorem to demonstrate the estimation potential for a fixed point of the cutter and the finite general split feasibility problem. Consequently, the set of fixed points of a quasi-nonexpansive mapping and the finite general split feasibility problem, the constrained minimization problem, and the general constrained minimization problems are proved using our main results. Finally, we give two numerical examples to advocate our main 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.
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Application of The Combination of Variational Inequalities for Fixed Point Problems and Optimization Problems
(2022-03-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
In this paper, we obtain a strong convergence theorem for finding a common element of the set of solutions of variational inequality problems and equilibrium problems. Moreover, we apply our main result to obtain a strong convergence theorem for finding a common element of the set of fixed point problems of strictly pseudo-contractive mappings and a convergence theorem involving minimization problems. Furthermore, we utilize our main theorem for numerical examples.

Kangtunyakarn, Atid

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