Kangtunyakarn, Atid

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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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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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Strong convergence of the hybrid method for a finite family of nonspreading mappings and variational inequality problems
(2012-01-01)
Kangtunyakarn, Atid
In this paper, we prove a strong convergence theorem by the hybrid method for finding a common element of the set of fixed points of a finite family of nonspreading mappings and the set of solutions of a finite family of variational inequality problems. © 2012 Kangtunyakarn; licensee Springer.
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On Approximation of the Combination of Variational Inequality Problem and Equilibrium Problem for Nonlinear Mappings
(2021-12-01)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
Using the concept of the combination of equilibrium problem, we introduce the combination of variational inequality problem for a finite family of inverse-strongly monotone mappings. Under some control conditions, we prove the strong convergence theorem for these nonlinear problems and fixed points of nonspreading mapping. Finally, we give numerical examples in two-dimensional space of real numbers in order to compare numerical results between the combination of variational inequality problem and the variational inequality problem.
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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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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.
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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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