• Title/Summary/Keyword: vector valued inequalities

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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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WEIGHTED ESTIMATES FOR CERTAIN ROUGH OPERATORS WITH APPLICATIONS TO VECTOR VALUED INEQUALITIES

  • Liu, Feng;Xue, Qingying
    • Journal of the Korean Mathematical Society
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    • v.58 no.4
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    • pp.1035-1058
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    • 2021
  • Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.

REGULARITY OF NONLINEAR VECTOR VALUED VARIATIONAL INEQUALITIES

  • Kim, Do-Wan
    • Journal of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.565-577
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    • 2000
  • We consider regularity questions arising in the degenerate elliptic vector valued variational inequalities -div(|▽u|p-2∇u)$\geq$b(x, u, ∇u) with p$\in$(1, $\infty$). It is a generalization of the scalar valued inequalities, i.e., the obstacle problem. We obtain the C1,$\alpha$loc regularity for the solution u under a controllable growth condition of b(x, u, ∇u).

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INTERVAL VALUED VECTOR VARIATIONAL INEQUALITIES AND VECTOR OPTIMIZATION PROBLEMS VIA CONVEXIFICATORS

  • TIRTH RAM;ROHIT KUMAR BHARDWAJ
    • Journal of applied mathematics & informatics
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    • v.41 no.6
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    • pp.1419-1432
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    • 2023
  • In this study, we take into account interval-valued vector optimization problems (IVOP) and obtain their relationships to interval vector variational inequalities (IVVI) of Stampacchia and Minty kind in aspects of convexificators, as well as the (IVOP) LU-efficient solution under the LU-convexity assumption. Additionally, we examine the weak version of the (IVVI) of the Stampacchia and Minty kind and determine the relationships between them and the weakly LU-efficient solution of the (IVOP). The results of this study improve and generalizes certain earlier results from the literature.

Some generalized weak vector quasivariational-like inequalities for fuzzy mappings

  • Lee Byung-Soo;Cho Hyun-Duk
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.6 no.1
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    • pp.70-76
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    • 2006
  • Some Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings was introduced and the existence of solutions to them under non-compact assumption was considered using the particular form of the generalized Ky Fan's section theorem due to Park [15]. As a corollary, Stampacchia type of generalized vector quasivariational-like inequalities for fuzzy mappings was studied under compact assumption using Ky Fan's section theorem [7].

GENERALIZED FUZZY WEAK VECTOR QUASIVARIATIONAL-LIKE INEQUALITIES

  • LEE, BYUNG-SOO
    • Honam Mathematical Journal
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    • v.27 no.3
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    • pp.445-463
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    • 2005
  • In this paper, we introduce a Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings and consider the existence of solutions to them under non-compact assumption.

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PROPER EFFICIENCY FOR SET-VALUED OPTIMIZATION PROBLEMS AND VECTOR VARIATIONAL-LIKE INEQUALITIES

  • Long, Xian Jun;Quan, Jing;Wen, Dao-Jun
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.777-786
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    • 2013
  • The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.