Kangtunyakarn, Atid

Preferred name

Kangtunyakarn, Atid

Alternative Name

Kangtunyakarn, A.

Main Affiliation

School of Science

atid.ka@kmitl.ac.th

Now showing 1 - 10 of 14

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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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Iterative algorithms for finding a common solution of system of the set of variational inclusion problems and the set of fixed point problems
(2011-01-01)
Kangtunyakarn, Atid
In this article, we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping, we prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of nonexpansive mappings and the set of a finite family of variational inclusion problems in Hilbert space. In the last section, we apply our main result to prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of strictly pseudocontractive mappings and the set of finite family of variational inclusion problems. © 2011 Kangtunyakarn; licensee Springer.
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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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Iterative approximation of common element of solution sets of various nonlinear operator problems
(2013-01-01)
Kangtunyakarn, Atid
In this paper, we prove strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and the set of a finite family of the set of solution of equilibrium problems by using the new mapping generated by a finite family of nonexpansive mappings and a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and a sequences of positive real numbers. Furthermore, by using our main result, we obtain two interesting theorems involving variational inequality problems and variational inclusion problems. In the last section, we give numerical examples to support our main results. ©2013 Kangtunyakarn; licensee Springer.
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A theorem for solving Banach generalized system of variational inequality problems and fixed point problem in uniformly convex and 2-uniformly smooth Banach space
(2021-04-01)
Chaloemyotphong, Bunyawee
;
Kangtunyakarn, Atid
In this paper, we consider a Banach generalized system of variational inequality problems by using the concept of Kangtunyakarn (Fixed Point Theory Appl 2014:123, 2014) and showed the equivalence between a Banach generalized system of variational inequality problems and fixed point problems. And also, using modified viscosity iterative method, we prove a strong convergence theorem for finding a common solution of a Banach generalized system of variational inequality problems and fixed point problems for a nonexpansive mapping. The main theorem presented in this paper extend the corresponding result of variational inequality problems introduced by Aoyama et al. (Fixed Point Theory Appl 2006:35390, https://doi.org/10.1155/FPTA/2006/35390, 2006). Moreover, we give some numerical examples for supporting our main theorem.
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A new mapping for finding a common element of the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and two sets of variational inequalities in uniformly convex and 2-smooth Banach spaces
(2013-01-01)
Kangtunyakarn, Atid
In this paper we introduce a new mapping in a uniformly convex and 2-smooth Banach space to prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of fixed points of a finite family of strictly pseudo-contractive mappings and two sets of solutions of variational inequality problems. Moreover, we also obtain a strong convergence theorem for a finite family of the set of solutions of variational inequality problems and the set of fixed points of a finite family of strictly pseudo-contractive mappings by using our main result. © 2013 Kangtunyakarn; licensee Springer.
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Fixed point theory for nonlinear mappings in Banach spaces and applications
(2014-01-01)
Kangtunyakarn, Atid
The purpose of this research is to study a finite family of the set of solutions of variational inequality problems and to prove a convergence theorem for the set of such problems and the sets of fixed points of nonexpansive and strictly pseudo-contractive mappings in a uniformly convex and 2-uniformly smooth Banach space. We also prove a fixed point theorem for finite families of nonexpansive and strictly pseudo-contractive mappings in the last section. © 2014 Kangtunyakarn; licensee Springer.
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The new variational inclusion problems for fixed point theorem
(2015-01-01)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
For the purpose of this article, we modify the variational inclusion problems and prove the strong convergence theorem for approximating a common element of two sets of solutions of variational inclusion problems, variational inequality problem and the set of fixed points of a nonexpansive mapping without the conditions ∑<inf>n=l</inf><sup>∞</sup> α<inf>n</inf> = ∞ and lim<inf>n→∞</inf>α<inf>n</inf> = 0 in a framework of Hilbert space.
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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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The modification of system of variational inequalities for fixed point theory in Banach spaces
(2014-01-01)
Kangtunyakarn, Atid
In this paper, we use methods different from extragradient methods to prove a strong convergence theorem for the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and the set of solutions of modification of a system of variational inequalities problems in a uniformly convex and 2-uniformly smooth Banach space. Applying the main result we obtain a strong convergence theorem involving two sets of solutions of variational inequalities problems introduced by Aoyama et al. (Fixed Point Theory Appl. 2006:35390, 2006, doi:10.1155/FPTA/2006/35390) in a uniformly convex and 2-uniformly smooth Banach space. We also give a numerical example to support our result. © 2014 Kangtunyakarn; licensee Springer.

Kangtunyakarn, Atid

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