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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A new iterative scheme for fixed point problems of infinite family of κ i-pseudo contractive mappings, equilibrium problem, variational inequality problems
(2013-08-01)
Kangtunyakarn, Atid
In this paper, we modify the set of variational inequality to construct a new iterative scheme for finding a common element of the set of fixed point problems of infinite family of κ <inf>i</inf> -pseudo-contractive mappings and the set of equilibrium problem and two set of variational inequality problems. © 2012 Springer Science+Business Media, LLC.
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Convergence theorem for solving the combination of equilibrium problems and fixed point problems in Hilbert spaces
(2016-01-01)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
In this article, we propose an iterative algorithm for approximating a common element of solution sets of equilibrium problems, the fixed point sets of nonspreading mappings and the fixed point sets of κ<inf>i</inf>-strictly pseudo contractive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative scheme converges strongly to a common element of those three sets. Finally, to support our main results, the numerical examples are given.
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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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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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Convergence theorems for a system of equilibrium problems and fixed point problems of a strongly nonexpansive sequence
(2013-01-01)
Kangtunyakarn, Atid
The purpose of this paper is to prove a strong convergence theorem of an iterative scheme associated to a strongly nonexpansive sequence for finding a common element of the set of equilibrium problems and the set of fixed point problems of a pair of sequences of nonexpansive mappings where one of them is a strongly nonexpansive sequence. Moreover, in the last section, by using our main result, we obtain a strong convergence theorem of an iterative scheme associated to a strongly nonexpansive sequence for finding a common element of the set of a finite family of equilibrium problems and the set of fixed point problems of a pair of sequences of nonexpansive mappings where one of them is a strongly nonexpansive sequence in a Hilbert space, and we also give some examples to support our main result. © 2013 Kangtunyakarn; licensee Springer.
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The split combination of variational inequalities for fixed point theory of a finite family of nonspreading mappings
(2017-10-01)
Kangtunyakarn, Atid
In this research, we introduced the split combination of variational inequality problem inspired by the reseach of Kangtunyakarn (Fixed Point Theory Appl 2013:171, 2013) and Censer (Numer Algorithms 59(2):301–323, 2012). Then we prove strong convergence theorem for finding a common element of the sets of fixed points of a finite family of nonspreading mapping and the sets of solutions of such a problem. Moreover, we also prove a convergence theorem involving two split variation inequality problems by using our main results.
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A new approximation method for finding common elements of equilibrium problems, variational inequality problems and fixed point problems of nonspreading mappings
(2017-10-01)
Cheawchan, Kanyarat
;
Phuengrattana, Withun
;
Kangtunyakarn, Atid
In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of the equilibrium problem, the set of solutions of the variational inequality problem and the set of fixed points of a nonspreading mapping in Hilbert spaces. Under suitable assumptions, weak convergence theorems have been proved in the framework of a Hilbert space. Our results improve and extend the corresponding results existing in the current literature. In addition, a numerical result indicate that the proposed method is quite effective.
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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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Iterative approximation method for various nonlinear mappings and equilibrium problems with numerical example
(2017-01-01)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
In this paper, we prove strong convergence of a new iterative algorithm for finding a common element of the set of fixed points of a finite family of nonspreading mappings, the set of solutions of a finite family of equilibrium problems and the set of solutions of two variational inequality problems in a real Hilbert space. In the last section, we give the numerical example to support our result.

Kangtunyakarn, Atid

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