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 10

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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 three-intermixed algorithm for common fixed point problems with applications to convex optimization and network allocation
(2026-07-01)
Saechou, Kanyanee
;
Kangtunyakarn, Atid
This study investigates a new algorithm, termed the three-intermixed algorithm, developed from the intermixed algorithm introduced by Yao et al. (Fixed Point Theory Appl 206, 2015). A strong convergence theorem is established for finding a common element in the set of fixed points of nonexpansive mappings. To illustrate our main theorem, we provide an example in R2 along with a graphical representation showing the behavior of the sequences {xn},{yn}, and {zn}. Beyond theoretical development, the applicability of the main theorem is demonstrated through several important problems, including the convex minimization problem, the split feasibility problem, and both general and new systems of variational inequality problems. In addition, a special case of the main theorem is applied to the network bandwidth allocation problem. A detailed numerical example is presented to show how the proposed iterative scheme can be used to compute a proportionally fair allocation under capacity and minimum rate constraints, thereby confirming the practical efficiency of the method.
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Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions
(2018-01-01)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
The purpose of this article, we give a necessary and sufficient condition for the modified Mann iterative process in order to obtain a strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and variational inequality problem in Hilbert space without the conditions (Formula presented). Moreover, we utilize our main result to fixed point problems of strictly pseudocontractive mappings and the set of solutions of variational inequality problem.
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A method for solving the variational inequality problem and fixed point problems in Banach spaces
(2021-04-14)
Khuangsatung, Wongvisarut
;
Kangtunyakarn, Atid
The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.
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Iterative approximation of common element of solution sets of various nonlinear operator problems
(2013-01-01)
Kangtunyakarn, Atid
In this paper, we prove strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and the set of a finite family of the set of solution of equilibrium problems by using the new mapping generated by a finite family of nonexpansive mappings and a finite family of κ<inf>i</inf>-strictly pseudocontractive mappings and a sequences of positive real numbers. Furthermore, by using our main result, we obtain two interesting theorems involving variational inequality problems and variational inclusion problems. In the last section, we give numerical examples to support our main results. ©2013 Kangtunyakarn; licensee Springer.
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Convergence theorem of κ-strictly pseudocontractive mapping and a modification of generalized equilibrium problems
(2012-12-01)
Kangtunyakarn, Atid
The purpose of this article, we first introduce strong convergence theorem of κ-strictly pseudo-contractive mapping without assumption of the mapping S = κ + (1 - κ)T. Then, we prove strong convergence of proposed iterative scheme for finding a common element of the set of fixed points of κ-strictly pseudo-contractive mapping and the set of solution of a modification of generalized equilibrium problem. Moreover, by using our main result and a new lemma in the last section we obtain strong convergence theorem for finding a common element of the set of fixed points of/c-strictly pseudo-contractive mapping and two sets of solutions of variational inequalities. © 2012 Kangtunyakarn; licensee Springer.
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A theorem for solving Banach generalized system of variational inequality problems and fixed point problem in uniformly convex and 2-uniformly smooth Banach space
(2021-04-01)
Chaloemyotphong, Bunyawee
;
Kangtunyakarn, Atid
In this paper, we consider a Banach generalized system of variational inequality problems by using the concept of Kangtunyakarn (Fixed Point Theory Appl 2014:123, 2014) and showed the equivalence between a Banach generalized system of variational inequality problems and fixed point problems. And also, using modified viscosity iterative method, we prove a strong convergence theorem for finding a common solution of a Banach generalized system of variational inequality problems and fixed point problems for a nonexpansive mapping. The main theorem presented in this paper extend the corresponding result of variational inequality problems introduced by Aoyama et al. (Fixed Point Theory Appl 2006:35390, https://doi.org/10.1155/FPTA/2006/35390, 2006). Moreover, we give some numerical examples for supporting our main theorem.
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A new mapping for finding a common element of the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and two sets of variational inequalities in uniformly convex and 2-smooth Banach spaces
(2013-01-01)
Kangtunyakarn, Atid
In this paper we introduce a new mapping in a uniformly convex and 2-smooth Banach space to prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of fixed points of a finite family of strictly pseudo-contractive mappings and two sets of solutions of variational inequality problems. Moreover, we also obtain a strong convergence theorem for a finite family of the set of solutions of variational inequality problems and the set of fixed points of a finite family of strictly pseudo-contractive mappings by using our main result. © 2013 Kangtunyakarn; licensee Springer.
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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 scheme for a nonexpansive mapping, an η-strictly pseudo-contractive mapping and variational inequality problems in a uniformly convex and 2-uniformly smooth Banach space
(2013-01-01)
Kangtunyakarn, Atid
In this paper, we introduce an iterative scheme by the modification of Mann's iteration process for finding a common element of the set of solutions of a finite family of variational inequality problems and the set of fixed points of an η-strictly pseudo-contractive mapping and a nonexpansive mapping. Moreover, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of η<inf>i</inf>-strictly pseudo-contractive mappings for every i = 1,2, . . . , N in uniformly convex and 2-uniformly smooth Banach spaces. © 2013 Kangtunyakarn; licensee Springer.

Kangtunyakarn, Atid

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