Narin Petrot
, Phitsanulok

Analysis

Ph. D.
25.95

Publications

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    ABSTRACT: The main objective of this paper is to introduce a split hierarchical variational inequality problem. Several related problems are also considered. We propose an iterative method for finding a solution of our problem. The weak convergence of the sequence generated by the proposed method is studied.
    Fixed Point Theory and Applications 10/2014; DOI:10.1186/1687-1812-2014-208 · 2.49 Impact Factor
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    Nimit Nimana, Narin Petrot
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    ABSTRACT: The main objective of this paper is to find a common solution of split variational inclusion problem and fixed point problem of infinite family of nonexpansive operators in a setting of real Hilbert spaces. To reach this goal, the iterative algorithms which combine Moudafi's viscosity approximation method with some fixed point technically proving methods are utilized for solving the problem. We prove that the iterative schemes with some suitable control conditions converge strongly to a common solution of the considered problem. We also show that many interesting problems can be solved by using our presented results. Index Terms—Split variational inclusion problem, fixed point problem, nonexpansive operators, resolvent operators, strong convergence.
    International MultiConference of Engineers and Computer Scientists 2014, Hong Kong; 03/2014
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    ABSTRACT: In this paper, we present some fixed-point theorems that are related to a set-valued Caristi-type mapping. The main results extend the recent work which was presented by Jiang and Li (Fixed Point Theory Appl. 2013:74, 2013) from a single-valued setting to a set-valued case. Further, the presented results also improve essentially many results that have appeared, because we have removed some conditions from the auxiliary function. Meanwhile, we give some partial answers to an important problem which was raised by Kirk (Colloq. Math. 36:81-86, 1976). MSC: Primary 47H10; secondary 37C25
    Fixed Point Theory and Applications 02/2014; DOI:10.1186/1687-1812-2014-27 · 2.49 Impact Factor
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    ABSTRACT: In this paper, a multivalued variational inequality problem on uniformly prox-regular set is studied. The existence theorems for such aforementioned problem are presented and, consequently, some algorithms for finding those solutions are also constructed. The results in this paper can be viewed as an improvement of the significant result that presented in Bounkhel et al. (J Inequal Pure Appl Math 4(1), 2003, Article 14).
    Optimization Letters 01/2014; 8(1). DOI:10.1007/s11590-012-0545-x · 0.99 Impact Factor
  • Narin Petrot, Jittiporn Suwannawit
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    ABSTRACT: This paper deals with some existence results for a class of systems of quasi-variational inequality problems. The setting corresponds to uniformly prox-regular sets. The authors establish some sufficient conditions to guarantee the existence of solutions. The arguments rely on elementary techniques in the theory of variational inequalities.
    Mathematical Inequalities and Applications 10/2013; 16(4). DOI:10.7153/mia-16-95 · 0.49 Impact Factor
  • Jittiporn Suwannawit, Narin Petrot
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    ABSTRACT: The concept of quasivariational inequality problem on proximally smooth sets is studied. Some sufficient conditions for solving the existence of solutions of such a problem are provided; also some interesting cases are discussed. Of course, due to the significance of proximally smooth sets, the results which are presented in this paper improve and extend many important results in the literature.
    Abstract and Applied Analysis 01/2013; 2013. DOI:10.1155/2013/612819 · 1.27 Impact Factor
  • Narin Petrot, Javad Balooee
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    ABSTRACT: In this paper, we introduce and consider a new system of generalized nonlinear mixed variational inequalities involving six different nonlinear operators and discuss the existence and uniqueness of solution of the aforesaid system. We use three nearly uniformly Lipschitzian mappings S i (i=1,2,3) to suggest and analyze some new three-step resolvent iterative algorithms with mixed errors for finding an element of the set of fixed points of the nearly uniformly Lipschitzian mapping Q=(S 1 ,S 2 ,S 3 ), which is the unique solution of the system of generalized nonlinear mixed variational inequalities. The convergence analysis of the suggested iterative algorithms under suitable conditions is studied. In the final section, an important remark on a class of some relaxed cocoercive mappings is discussed.
    Fixed Point Theory and Applications 01/2013; 2013. DOI:10.1186/1687-1812-2013-186 · 2.49 Impact Factor
  • Narin Petrot, Javad Balooee
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    ABSTRACT: The paper presents an existence and uniqueness result for a system of generalized nonlinear variational inclusions in q-uniformly smooth Banach space. A perturbed iterative algorithm with mixed errors is also given. The approach is based on the resolvent operator technique.
    Journal of Computational Analysis and Applications 01/2013; 15(1). · 0.72 Impact Factor
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    Narin Petrot, Javad Balooee
    Journal of Computational Analysis and Applications 01/2013; 15(1). · 0.72 Impact Factor
  • Narin Petrot, Javad Balooee
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    ABSTRACT: In this paper, we introduce and study a new system of general nonconvex variational inclusions involving four different nonlinear operators (SGNVI) and prove the equivalence between the SGNVI and a fixed point problem. By using this equivalent formulation, we establish the existence and uniqueness theorem for solutions of the SGNVI. We use the foregoing equivalent alternative formulation and two nearly uniformly Lipschitzian mappings S 1 and S 2 to suggest and analyze some new two-step projection iterative algorithms for finding an element of the set of fixed points of the nearly uniformly Lipschitzian mapping Q=(S 1 ,S 2 ), which is the unique solution of the SGNVI. Further, the convergence analysis of the suggested iterative algorithms under suitable conditions is studied.
    Journal of Inequalities and Applications 01/2013; 2013. DOI:10.1186/1029-242X-2013-377 · 0.77 Impact Factor
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    Yeol Je Cho, Narin Petrot
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    ABSTRACT: In this paper, we provide a regularization method for finding a solution of Noor’s variational inequality problem induced by a hemicontinuous monotone operator. Moreover, such a solution is related to the set of zero of inverse strongly monotone mappings. Consequently, since we do not assume the strong monotonicity of the considered operator, our results are general and extend some well-known results in the literature.
    Fixed Point Theory and Applications 01/2012; 2012(1). DOI:10.1186/1687-1812-2012-169 · 2.49 Impact Factor
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    Narin Petrot, Javad Balooee
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    ABSTRACT: At the present article, we consider a new class of general nonlinear random A-maximal m-relaxed η-accretive equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By using the resolvent mapping technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang's lemma, we construct a new iterative algorithm with mixed errors for finding the approximate solutions of this class of nonlinear random equations. We also verify that the approximate solutions obtained by the our proposed algorithm converge to the exact solution of the general nonlinear random A-maximal m-relaxed η-accretive equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. Mathematical Subject Classification 2010: Primary, 47B80; Secondary, 47H40, 60H25.
    Journal of Inequalities and Applications 01/2012; 2012(1). DOI:10.1186/1029-242X-2012-98 · 0.77 Impact Factor
  • Narin Petrot, Javad Balooee
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    ABSTRACT: We introduce a new system of extended general nonlinear variational inclusions with different nonlinear operators and establish the equivalence between the aforesaid system and the fixed point problem. By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. We suggest and analyze a new resolvent iterative algorithm to approximate the unique solution of the system of extended general nonlinear variational inclusions which is a fixed point of a nearly uniformly Lipschitzian mapping. Subsequently, the convergence analysis of the proposed iterative algorithm under some suitable conditions is considered. Furthermore, some related works to our main problem are pointed out and discussed.
    Abstract and Applied Analysis 01/2012; 2012. DOI:10.1155/2012/569592 · 1.27 Impact Factor
  • Jittiporn Suwannawit, Narin Petrot
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    ABSTRACT: We introduce and study a class of a system of random set-valued variational inclusionproblems. Some conditions for the existence of solutions of such problems are provided, when the operatorsare contained in the classes of generalized monotone operators, so-called ($A,m,\eta $)-monotone operator. Further,the stability of the iterative algorithm for finding a solution of the considered problem is also discussed.
    Journal of Applied Mathematics 01/2012; 2012, Special Issue. DOI:10.1155/2012/590676 · 0.72 Impact Factor
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    ABSTRACT: In this paper, the concept of a set-valued contractive mapping is considered by using the idea of a generalized distance, such as the τ-distance, in metric spaces without using the concept of the Hausdorff metric. Furthermore, under some mild conditions, we provide the existence theorems for fixed-point problems of the considered mapping. Hence, our results can be viewed as a generalization and improvement of many recent results.
    Applied Mathematics Letters 11/2011; 24(11):1959-1967. DOI:10.1016/j.aml.2011.05.030 · 1.48 Impact Factor
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    Ravi P Agarwal, Yeol JE Cho, Narin Petrot
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    ABSTRACT: In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed) variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
    Fixed Point Theory and Applications 08/2011; 2011(1). DOI:10.1186/1687-1812-2011-31 · 2.49 Impact Factor
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    Yeol JE Cho, Narin Petrot
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    ABSTRACT: Without the strong monotonicity assumption of the mapping, we provide a regularization method for general variational inequality problem, when its solution set is related to a solution set of an inverse strongly monotone mapping. Consequently, an iterative algorithm for finding such a solution is constructed, and convergent theorem of the such algorithm is proved. It is worth pointing out that, since we do not assume strong monotonicity of general variational inequality problem, our results improve and extend some well-known results in the literature.
    Journal of Inequalities and Applications 07/2011; 2011(1). DOI:10.1186/1029-242X-2011-21 · 0.77 Impact Factor
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    Poom Kumam, Narin Petrot, Rabian Wangkeeree
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    ABSTRACT: In this paper, some existence theorems for the mixed quasi-variational-like inequalities problem in a reflexive Banach space are established. The auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi-variational-like inequalities problem. Consequently, not only the existence of theorems of the mixed quasi-variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is also proven. The results proved in this paper represent an improvement of previously known results.
    Applied Mathematics and Computation 05/2011; 217:7496-7503. DOI:10.1016/j.amc.2011.02.054 · 1.60 Impact Factor
  • Suthep Suantai, Narin Petrot
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    ABSTRACT: In this paper, we consider the system of nonlinear quasi-mixed equilibrium problems. The existence theorems of solutions of such problems are provided by considering the limit point of an iterative algorithm. This means, we not only give the conditions for the existence theorems of the presented problems but also provide the algorithm to find such solutions. Moreover, the stability of such an algorithm is also discussed. The results presented in this paper are more general, and may be viewed as an extension, refinement and improvement of the previously known results in the literature.
    Applied Mathematics Letters 03/2011; 24(3):308-313. DOI:10.1016/j.aml.2010.10.011 · 1.48 Impact Factor
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    Yeol-Je Cho, Narin Petrot
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    ABSTRACT: In this paper, some fuzzy fixed point theorems for fuzzy mappings are established by considering the nonempty closed -cut sets. Some importance observations are also discussed. Our results clearly extend, generalize and improve the corresponding results in the literatures, which have given most of their attention to the class of fuzzy sets with nonempty compact or closed and bounded -cut sets.
    Communications of the Korean Mathematical Society 01/2011; 26(1). DOI:10.4134/CKMS.2011.26.1.115

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