Kangtunyakarn, Atid

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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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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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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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Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings
(2014-01-01)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem. © 2014 Suwannaut and 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 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
(2013-01-01)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
For the purpose of this article, we introduce a new problem using the concept of equilibrium problem and prove the strong convergence theorem for finding a common element of the set of fixed points of an infinite family of κ<inf>i</inf>-strictly pseudo contractive mappings and of a finite family of the set of solutions of equilibrium problem and variational inequalities problem. Furthermore, we utilize our main theorem for the numerical example. ©2013 Suwannaut and Kangtunyakarn; licensee Springer.
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Convergence analysis for the equilibrium problems with numerical results
(2014-12-22)
Suwannaut, Sarawut
;
Kangtunyakarn, Atid
In this paper, we propose an iterative scheme modified from the work of Ceng et al. (Nonlinear Anal. Hybrid Syst. 4:743-754, 2010) and Plubtieng and Punpaeng (J. Math. Anal. Appl. 336(1):455-469, 2007) to prove the strong convergence theorem for approximating a common element of the set of fixed points of nonspreading mappings and a finite family of the set of solutions of the equilibrium problem. Using this result, we obtain the strong convergence theorem for a finite family of nonspreading mappings and a finite family of the set of solutions of equilibrium problem. Moreover, in order to compare numerical results between the combination of the equilibrium problem and the classical equilibrium problem, some examples are given in one- and two-dimensional spaces of real numbers.
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The Iterative Method for Generalized Equilibrium Problems and a Finite Family of Lipschitzian Mappings in Hilbert Spaces
(2022-01-01)
Kangtunyakarn, Atid
;
Suwannaut, Sarawut
In this research, we introduced the S-mapping generated by a finite family of contractive mappings, Lipschitzian mappings and finite real numbers using the results of Kangtunyakarn (2013). Then, we prove the strong convergence theorem for fixed point sets of finite family of contraction and Lipschitzian mapping and solution sets of the modified generalized equilibrium problem introduced by Suwannaut and Kangtunyakarn (2014). Finally, numerical examples are provided to illustrate our main theorem.

Kangtunyakarn, Atid

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