• Title, Summary, Keyword: quasi­variational inequalities

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MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • Lee Byung-Soo
    • The Pure and Applied Mathematics
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    • v.13 no.3
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    • pp.197-206
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    • 2006
  • This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

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GENERALIZED VECTOR-VALUED VARIATIONAL INEQUALITIES AND FUZZY EXTENSIONS

  • Lee, Byung-Soo;Lee, Gue-Myung;Kim, Do-Sang
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.609-624
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    • 1996
  • Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

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GENERALIZED NONLINEAR MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • Lee, Byung-Soo;Khan M. Firdosh;Salahuddin Salahuddin
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.689-700
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    • 2006
  • In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI

  • Kum, Sangho
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.1
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    • pp.145-150
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    • 2015
  • Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

MIXED QUASI VARIATIONAL INEQUALITIES INVOLVING FOUR NONLINEAR OPERATORS

  • Pervez, Amjad;Khan, Awais Gul;Noor, Muhammad Aslam;Noor, Khalida Inayat
    • Honam Mathematical Journal
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    • v.42 no.1
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    • pp.17-35
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    • 2020
  • In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the fixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.

GENERALIZED BI-QUASI-VARIATIONAL-LIKE INEQUALITIES ON NON-COMPACT SETS

  • Cho, Yeol Je;Chowdhury, Mohammad S.R.;Ha, Je Ai
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.933-957
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    • 2017
  • In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

ON GENERALIZED VECTOR QUASI-VARIATIONAL TYPE INEQUALITIES

  • Cho, Y.J.;Salahuddin, Salahuddin;Ahmad, M.K.
    • East Asian mathematical journal
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    • v.26 no.1
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    • pp.49-58
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    • 2010
  • In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

COMPARISON EXAMPLES ON GENERALIZED QUASI-VARIATIONAL INEQUALITIES

  • Kum, Sang-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.371-377
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    • 1999
  • The purpose of this paper is to provide two examples which prove that Cubiotti's theorem and Yao's one on the generalized quasi-variational inequality problem are independent of each other. In addition, we give another example which tells us that certain conditions are essential in Cubiotti's theorem and Yao's one.

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