• 제목/요약/키워드: education inequality

검색결과 407건 처리시간 0.021초

STRONG LAW OF LARGE NUMBERS FOR ASYMPTOTICALLY NEGATIVE DEPENDENT RANDOM VARIABLES WITH APPLICATIONS

  • Kim, Hyun-Chull
    • Journal of applied mathematics & informatics
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    • 제29권1_2호
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    • pp.201-210
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    • 2011
  • In this paper, we obtain the H$\`{a}$jeck-R$\`{e}$nyi type inequality and the strong law of large numbers for asymptotically linear negative quadrant dependent random variables by using this inequality. We also give the strong law of large numbers for the linear process under asymptotically linear negative quadrant dependence assumption.

ON THE EXPONENTIAL INEQUALITY FOR NEGATIVE DEPENDENT SEQUENCE

  • Kim, Tae-Sung;Kim, Hyun-Chull
    • 대한수학회논문집
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    • 제22권2호
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    • pp.315-321
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    • 2007
  • We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.

A REFINEMENT OF LYAPUNOV-TYPE INEQUALITY FOR A CLASS OF NONLINEAR SYSTEMS

  • Kim, Yong-In
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제18권4호
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    • pp.329-336
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    • 2011
  • Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.

MINTY'S LEMMA FOR STRONG IMPLICIT VECTOR VARIATIONAL INEQUALITY SYSTEMS

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제15권4호
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    • pp.423-432
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    • 2008
  • In this paper, we consider a new Minty's Lemma for strong implicit vector variational inequality systems and obtain some existence results for systems of strong implicit vector variational inequalities which generalize some results in [1].

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ERROR BOUNDS FOR NONLINEAR MIXED VARIATIONAL-HEMIVARIATIONAL INEQUALITY PROBLEMS

  • A. A. H. Ahmadini;Salahuddin;J. K. Kim
    • Nonlinear Functional Analysis and Applications
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    • 제29권1호
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    • pp.15-33
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    • 2024
  • In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

REFINEMENT OF HERMITE HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH APPLICATIONS

  • Muhammad Bilal;Asif R. Khan
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제31권1호
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    • pp.33-48
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    • 2024
  • In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

CONVERGENCE OF MODIFIED VISCOSITY INEXACT MANN ITERATION FOR A FAMILY OF NONLINEAR MAPPINGS FOR VARIATIONAL INEQUALITY IN CAT(0) SPACES

  • Kyung Soo Kim
    • Nonlinear Functional Analysis and Applications
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    • 제28권4호
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    • pp.1127-1143
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    • 2023
  • The purpose of this paper, we prove convergence theorems of the modified viscosity inexact Mann iteration process for a family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. We also show that the limit of the modified viscosity inexact Mann iteration {xn} solves the solution of some variational inequality.

AN EXTENSION OF GENERALIZED VECTOR QUASI-VARIATIONAL INEQUALITY

  • Kum Sang-Ho;Kim Won-Kyu
    • 대한수학회논문집
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    • 제21권2호
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    • pp.273-285
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    • 2006
  • In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.