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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Hybrid algorithm for finding common elements of the set of generalized equilibrium problems and the set of fixed point problems of strictly pseudocontractive mapping
(2011-03-07)
Kangtunyakarn, Atid
The purpose of this paper is to prove the strong convergence theorem for finding a common element of the set of fixed point problems of strictly pseudocontractive mapping in Hilbert spaces and two sets of generalized equilibrium problems by using the hybrid method. Copyright © 2011 Atid Kangtunyakarn.
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The theory of the feasibility problems and fixed point problems of nonlinear mappings
(2019-08-01)
Premjitpraphan, Sirawit
;
Kangtunyakarn, Atid
In this paper, the authors extend and improve some results of Hamdi [Hamdi, A., Liou, Y.C., Yao, Y. and Luo, C.: The common solutions of the split feasibility problems and fixed point problems. Journal of Inequalities and Applications (2015) 2015:385 DOI10.1186/s13660-015-0870-6] by using the concept of lemma 2.11 Suwannaut and Kangtunyakarn [Suwannaut, S. and Kangtunyakarn, A.: The combination of the set of solutions of equilibrium problem for convergence theorem of the set of fixed points of strictly pseudo-contractive mappings and variational inequalities problem. Fixed Point Theory and its Applications (2013) 2013:291]. Then they prove strong convergence theorem of the proposed iteration under some control condition. Moreover, we use S-mapping in application with our main result.
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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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Convergence theorem of two sequences for solving the modified generalized system of variational inequalities and numerical analysis
(2019-10-01)
Sripattanet, Anchalee
;
Kangtunyakarn, Atid
The purpose of this paper is to introduce an iterative algorithm of two sequences which depend on each other by using the intermixed method. Then, we prove a strong convergence theorem for solving fixed-point problems of nonlinear mappings and we treat two variational inequality problems which form an approximate modified generalized system of variational inequalities (MGSV). By using our main theorem, we obtain the additional results involving the split feasibility problem and the constrained convex minimization problem. In support of our main result, a numerical example is also presented.
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Convergence theorem of common fixed points for a family of nonspreading mappings in Hilbert space
(2012-06-01)
Kangtunyakarn, Atid
We introduce the concept of K-mapping of a finite family of nonspreading mappings {T <inf>i</inf>} <sup>N</sup> <inf>i=1</inf> and we show that the fixed point set of the K-mapping is the set of common fixed points of {T <inf>i</inf>} <sup>N</sup> <inf>i=1</inf>. Moreover, we prove strong convergence theorem of the Ishikawa iterative process to a common fixed point of a finite family of nonspreading mappings in Hilbert space under certain control conditions. © 2011 Springer-Verlag.
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Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph
(2018-04-01)
Kangtunyakarn, Atid
The aim of this research is to introduce G–S-mapping generated by a finite family of G-nonexpansive mappings and finite real numbers and prove a convergence theorem of Halpern iteration associated with G–S-mapping for fixed point problem of a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graph, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 2015:187, 2015). Moreover, we introduce a new method for the estimation of value of π using our theorem.
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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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An intermixed algorithm for solving fixed point problems of proximal operators in Hilbert Spaces
(2024-01-01)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
The aim of this paper is to modify proximal operators in Hilbert spaces. We introduce an inter-mixed algorithm with viscosity technique to find the solution of fixed point problem of two proximal operators in a real Hilbert space, utilizing the modified proximal operators. Under some mild conditions, a strong convergence theorem is established for the proposed algorithm. We also apply our main result to the split feasibility problem. Finally we provide numerical examples for supporting the main result.
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The modification of generalized mixed equilibrium problems for convergence theorem of variational inequality problems and fixed point problems
(2021-03-01)
Khuangsatung, Wongvisarut
;
Suantai, Suthep
;
Kangtunyakarn, Atid
The purpose of this research, we modify generalized mixed equilibrium problems and prove a strong convergence theorem for approximating a common element of the set of such a problem and variational inequality problems and the set of fixed points of infinite family of strictly pseudo contractive mappings. Utilizing our main result, we also prove a strong convergence theorem involving generalized equilibrium problems and variational inequality problems.
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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.

Kangtunyakarn, Atid

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