Kangtunyakarn, Atid

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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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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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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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Hybrid iterative scheme for a generalized equilibrium problems, variational inequality problems and fixed point problem of a finite family of κi-strictly pseudocontractive mappings
(2012-12-01)
Kangtunyakarn, Atid
In this article, by using the S-mapping and hybrid method we prove a strong convergence theorem for finding a common element of the set of fixed point problems of a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and the set of generalized equilibrium defined by Ceng et al., which is a solution of two sets of variational inequality problems. Moreover, by using our main result we have a strong convergence theorem for finding a common element of the set of fixed point problems of a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and the set of solution of a finite family of generalized equilibrium defined by Ceng et al., which is a solution of a finite family of variational inequality problems. © 2012 Kangtunyakarn; licensee Springer.
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The method for solving variational inequality problems with numerical results
(2019-03-04)
Suwannaut, Sarawut
;
Suantai, Suthep
;
Kangtunyakarn, Atid
Using the concept of variational inequality method, we introduce the iterative scheme for finding a common element of the set of fixed point of a κ-strictly pseudo-contractive mapping and four sets of solutions of variational inequality problems. Furthermore, by using our main result, we give the numerical examples for supporting our results.
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An intermixed iteration for constrained convex minimization problem and split feasibility problem
(2019-01-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.
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Convergence theorem for solving a new concept of the split variational inequality problems and application
(2020-10-01)
Sripattanet, Anchalee
;
Kangtunyakarn, Atid
In this paper, we propose the split of modified variational inequality problems (SMVIP), by using the concept of the modified generalized system of variational inequalities (MGSV). Then, we prove the strong convergence theorem for solving fixed point problems of nonlinear mappings and two variational inequality problems and solving the SMVIP. Applying our main result, we prove strong convergence theorems of the split minimization problem and the split variational inequality problem. In support of our main result, a numerical example is also presented.
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Approximation method for fixed points of nonlinear mapping and variational inequalities with application
(2015-12-01)
Cheawchan, Kanyarat
;
Kangtunyakarn, Atid
In this paper, we introduce the new method of iterative scheme {x<inf>n</inf>} for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of a modified system of variational inequali- ties without demiclose condition and T<inf>ω</inf> := (1 − ω)I + ωT, when T is a quasi- nonexpansive mapping and ω ∈ (0, 1/2) in a framework of Hilbert space. Using our main result, we obtain strong convergence theorems involving a finite family of nonspreading mapping and another corollary.

Kangtunyakarn, Atid

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