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 88

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Method for Solving Variational Inequality Problems and Fixed Point Problems without Some Well-known Condition
(2024-01-01)
Nuisman, Anucha
;
Kangtunyakarn, Atid
This study presents an innovative method for approximating solutions to the variational inequality and fixed-point problems. The proposed approach deviates from traditional methods by employing different conditions and techniques drawn from [18] [20] [21]. Uniquely, our work circumvents the utilization of a commonly used lemma (see [10]) that forms the basis for most proofs related to strong convergence theorems. As part of our investigation, we provide a comprehensive numerical example to substantiate our findings, thus enhancing the practical relevance and applicability of our research.
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A new iterative algorithm for the set of fixed-point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem
(2011-06-22)
Kangtunyakarn, Atid
We introduce a new iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of fixed-point problems of infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of common fixed point of pseudocontractive mappings. Copyright © 2011 Atid Kangtunyakarn.
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Iterative methods for finding common solution of generalized equilibrium problems and variational inequality problems and fixed point problems of a finite family of nonexpansive mappings
(2010-12-01)
Kangtunyakarn, Atid
We introduce a new method for a system of generalized equilibrium problems, system of variational inequality problems, and fixed point problems by using S -mapping generated by a finite family of nonexpansive mappings and real numbers. Then, we prove a strong convergence theorem of the proposed iteration under some control condition. By using our main result, we obtain strong convergence theorem for finding a common element of the set of solution of a system of generalized equilibrium problems, system of variational inequality problems, and the set of common fixed points of a finite family of strictly pseudocontractive mappings. Copyright © 2010 Atid Kangtunyakarn.
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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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The existence theorem of a new multi-valued mapping in metric space endowed with graph
(2017-01-01)
Kheawborisut, Araya
;
Suantai, Suthep
;
Kangtunyakarn, Atid
In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.
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Iterative algorithms with the regularization for the constrained convex minimization problem and maximal monotone operators
(2017-10-03)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
In this paper, we prove a strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the set of solutions of a finite family of variational inclusion problems in Hilbert space. A strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the solution sets of a finite family of zero points of the maximal monotone operator problem in Hilbert space is also obtained. Using our main result, we have some additional results for various types of non-linear problems in Hilbert space.
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Strong convergence theorem for the split equality fixed point problem for quasi-nonexpansive mapping and application
(2019-01-01)
Premjitpraphan, S.
;
Kangtunyakarn, A.
Motivated by the work of Zhao [9], [10], [11] and by reducing some of his conditions, we consider a split equality fixed point problem for quasi-nonexpansive mappings which includes split feasibility problem, split equality problem, split fixed point problem, etc. The strong convergence theorem of the proposed iterative scheme could be obtained, under some control conditions. Furthermore, we use S-mapping applied to our main result to prove strong convergence theorems.
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Convergence analysis for relaxed extragradient method and variational inequality problem with numerical example
(2018-04-01)
Siriyan, Keerati
;
Kangtunyakarn, Atid
The purpose of this paper is to introduce an iterative method for finding a common element of fixed point of nonexpansive mapping which is generated by the general system of variational inequalities with inverse strongly monotone mappings and the set of the solution of variational inequality. By using our main result, we obtain the strong convergence theorem of the proposed iterative method and another corollary in a real Hilbert space.
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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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A new subgradient extragradient method for solving the split modified system of variational inequality problems and fixed point problem
(2022-01-01)
Sripattanet, Anchalee
;
Kangtunyakarn, Atid
We introduce a new subgradient extragradient algorithm utilizing the concept of the set of solutions of the split modified system of variational inequality problems (SMSVIP). Our main theorem is weak convergence theorem for such an algorithm for approximating the fixed point problem in a real Hilbert space. We also apply these results to approximate the split minimization problem. In the last section, we provide an example to illustrate the potential of our main theorem.

Kangtunyakarn, Atid

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