Kangtunyakarn, Atid

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Kangtunyakarn, Atid
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Kangtunyakarn, A.
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Email
atid.ka@kmitl.ac.th

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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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    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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    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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    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.