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 16

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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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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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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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Algorithm method for solving the split general system of variational inequalities problem and fixed point problem of nonexpansive mapping with application
(2018-01-01)
Siriyan, Keerati
;
Kangtunyakarn, Atid
The purpose of this research is to introduce the split general system of variational inequalities problem, by using the concept of the general system of variational inequalities problem in Ceng et al. Then, we establish and prove a strong convergence theorem for finding a common element of the set of solutions of this problem and the set of fixed points of a nonexpansive mapping for the first time in this research. By using ourmain theorem, strong convergence theorems of the split feasibility problem, the split variational inequality problem, and the minimization problem are obtained, respectively. In order to show the potential of our main result, we give three numerical examples of these classical problems introduced by previous studies, with the numerical example of our main theorem to compare the rate of convergence.
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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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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.
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The Three-step Intermixed Iteration for Two Finite Families of Nonlinear Mappings in a Hilbert Space
(2022-01-01)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
In this work, the three-step intermixed iteration for two finite families of non- linear mappings is introduced. We prove a strong convergence theorem for approximating a common fixed point of a strict pseudo-contraction and strictly pseudononspreading map- ping in a Hilbert space. Some additional results are obtained. Finally, a numerical example in a space of real numbers is also given and illustrated.
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Fixed point results in convex metric spaces
(2019-06-01)
Siriyan, Keerati
;
Kangtunyakarn, Atid
The purpose of this paper is to establish and prove a strong convergence theorem of Ishikawa iterative for finding a common fixed point of the combination of a finite family of nonexpansive mappings in a convex metric space. Moreover, our result generalizes and modifies the other result, Phuengrattana and Suantai’s result Phuengrattana and Suantai (Ind J Pure Appl Math 45(1):121–136, 2014).
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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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Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions
(2011-01-01)
Kangtunyakarn, Atid
In this article, we introduce a new mapping generated by an infinite family of κ<inf>i</inf>-strict pseudo-contractions and a sequence of positive real numbers. By using this mapping, we consider an iterative method for finding a common element of the set of a generalized equilibrium problem of the set of solution to a system of variational inequalities, and of the set of fixed points of an infinite family of strict pseudo-contractions. Strong convergence theorem of the purposed iteration is established in the framework of Hilbert spaces. © 2011 Kangtunyakarn; licensee Springer.

Kangtunyakarn, Atid

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