Narin Petrot
, Phitsanulok

Analysis

Ph. D.
26.27

Publications

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    Suthep Suantai · Narin Petrot · Warut Saksirikun
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    ABSTRACT: By using the concept of a class of functions, the R -functions, we provide some fuzzy fixed point theorems on a space of fuzzy sets equipped with the supremum metric. By presenting a technique of constructing a sequence of successive approximations, we obtain some interesting results that improve many existing results. The related cases are also shown and discussed. MSC: 47H10, 47S40, 54H25.
    Full-text · Article · Sep 2015 · Fixed Point Theory and Applications
  • L. Ćirić · Narin Petrot · Pornthip Promsinchai
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    ABSTRACT: By using a concept of generalized commuting mappings, we study a new cla.ss pair of mappings. Some fixed point theorems and corresponding example are considered and discussed on such introduced class. The presented results in this work are generalizations and improvements of many important results, in the sense that we are providing more choices of tool implements to check whether a fixed point of considered mapping exists.
    No preview · Article · Jan 2015 · Journal of nonlinear and convex analysis
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    Qamrul Hasan Ansari · Nimit Nimana · Narin Petrot
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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. MSC: 47H09, 47H10, 47J25, 49J40, 65K10.
    Full-text · Article · Oct 2014 · Fixed Point Theory and Applications
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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.
    Full-text · Conference Paper · Mar 2014
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    Nimit Nimana · Narin Petrot · Warut Saksirikun
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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: 47H10, 37C25.
    Full-text · Article · Feb 2014 · Fixed Point Theory and Applications
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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).
    Full-text · Article · Jan 2014 · Optimization Letters
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    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 solution of the SGNVI. We use the foregoing equivalent alternative formulation and two nearly uniformly Lipschitzian mappings S1 and S2 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 = (S1, S2), which is the unique solution of the SGNVI. Further, the convergence analysis of the suggested iterative algorithms under suitable conditions is studied.
    Preview · Article · Dec 2013 · Journal of Inequalities and Applications
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    Narin Petrot · Jittiporn Suwannawit
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    ABSTRACT: In this paper, some systems of quasi-variational inequality problems are considered on a class of nonconvex sets, as uniformly prox-regular sets. Some sufficient conditions for the existence solution of the considered problems are provided. Also, some interesting remarks are discussed. The results which are presented in this paper are more general, and may be viewed as an extension, improvement and refinement of the previously known results in the litterateurs.
    Full-text · Article · Oct 2013 · Mathematical Inequalities and Applications
  • 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 Si (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 = (S1, S2, S3), 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.
    No preview · Article · Jul 2013 · Fixed Point Theory and Applications
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    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.
    Full-text · Article · Feb 2013 · Abstract and Applied Analysis
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    Narin Petrot · Javad Balooee
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    ABSTRACT: At the present paper, the concept of a new contraction for set-valued maps in cone metric spaces with regular cone is introduced and two fixed point theorems for a such contraction are established. Two examples are given to show that our results are genuine generalizations of Wardowski's theorems.
    Full-text · Article · Jan 2013 · Journal of Computational Analysis and Applications
  • Narin Petrot · Javad Balooee
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    ABSTRACT: A new system of generalized nonlinear variational inclusions with A-maximal m-relaxed η-accretive (so called (A, η)-accretive [22]) mappings in q-uniformly smooth Banach spaces is introduced and studied. By using the resolvent operator technique associated with A-maximal m-relaxed η -accretive mappings due to Lan et al., the existence and uniqueness of solution for this system of generalized nonlinear variational inclusions is verified and a new perturbed iterative algorithm with mixed errors for solving the aforementioned system is constructed. Also the convergence of the sequences generated by the our algorithm in q-uniformly smooth Banach spaces is proved. The results presented in this paper extend and improve some known results in the literature.
    No preview · Article · Jan 2013 · Journal of Computational Analysis and Applications
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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.
    Full-text · Article · Oct 2012 · Fixed Point Theory and Applications
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    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.
    Full-text · Article · Aug 2012 · Abstract and Applied Analysis
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    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.
    Full-text · Article · May 2012 · Journal of Applied Mathematics
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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.
    Full-text · Article · Jan 2012 · Journal of Inequalities and Applications
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    Soawapak Hirunworakit · Narin Petrot
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    ABSTRACT: The purpose of this paper is to prove some existence theorems for fixed point problem by using a generalization of metric distance, namely u-distance. Consequently, some special cases are discussed and an interesting example is also provided. Presented results are generalizations of the important results due to Ume (Fixed Point Theory Appl 2010(397150), 21 pp, 2010) and Suzuki and Takahashi (Topol Methods Nonlinear Anal 8, 371-382, 1996). 2010 Mathematics Subject Classification: 47H09, 47H10.
    Full-text · Article · Nov 2011 · Fixed Point Theory and Applications
  • Yeol Je Cho · Soawapak Hirunworakit · Narin Petrot
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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.
    No preview · Article · Nov 2011 · Applied Mathematics Letters
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    ABSTRACT: In this paper, we introduce a general iterative approximation method for finding a common fixed point of a countable family of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. As applications, at the end of the paper, we apply our results to the problem of finding a zero of an accretive operator. The main result extends various results existing in the current literature.
    No preview · Article · Sep 2011 · Journal of Global Optimization
  • Source
    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.
    Full-text · Article · Aug 2011 · Fixed Point Theory and Applications

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