• Title, Summary, Keyword: inequalities

Search Result 1,111, Processing Time 0.038 seconds

GENERALIZED VECTOR-VALUED VARIATIONAL INEQUALITIES AND FUZZY EXTENSIONS

  • Lee, Byung-Soo;Lee, Gue-Myung;Kim, Do-Sang
    • Journal of the Korean Mathematical Society
    • /
    • v.33 no.3
    • /
    • pp.609-624
    • /
    • 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.

  • PDF

ON A NEW CLASS OF FUNCTIONS RELATED WITH MITTAG-LEFFLER AND WRIGHT FUNCTIONS AND THEIR PROPERTIES

  • Bansal, Deepak;Mehrez, Khaled
    • Communications of the Korean Mathematical Society
    • /
    • v.35 no.4
    • /
    • pp.1123-1132
    • /
    • 2020
  • In the present paper, we define new class of functions Tα,β(λ; z) which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Turán-type inequalities, Lazarević-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function Tα,β(λ; z) are presented.

ORLICZ-TYPE INTEGRAL INEQUALITIES FOR OPERATORS

  • Neugebauer, C.J.
    • Journal of the Korean Mathematical Society
    • /
    • v.38 no.1
    • /
    • pp.163-176
    • /
    • 2001
  • We examine Orlicz-type integral inequalities for operators and obtain as a corollary a characterization of such inequalities for the Hardy-Littlewood maximal operator extending the well-known L(sup)p-norm inequalities.

  • PDF

Health Inequalities in Korea: Current Conditions and Implications (한국 건강불평등의 현황과 문제점)

  • Kim, Yu-Mi;Kim, Myoung-Hee
    • Journal of Preventive Medicine and Public Health
    • /
    • v.40 no.6
    • /
    • pp.431-438
    • /
    • 2007
  • Objectives : The aim of this study is to summarize the current conditions and implications of health inequalities in South Korea. Methods : Through a literature review of empirical studies and supplementary analysis of the data presented in the 1998, 2001, and 2005 KNHANEs, we evaluated the extent and trends of socioeconomic inequalities in both health risk factors, such as smoking, physical activity, and obesity, and outcomes, such as total mortality, subjective poor health status by self-reports and metabolic syndrome. Relative risks and odds ratios were used to measure differences across socioeconomic groups, and the relative index of inequality was used to evaluate the changes in inequalities over time. Results : We found clear inequalities to various degrees?in most health indicators. While little change was observed in mortality differences over time, the socioeconomic gaps in risk factors and morbidity have been widening, with much larger differences among the younger population. Conclusions : Socioeconomic inequalities are pervasive across various health indicators, and some of them are increasing. The trends in socioeconomic inequalities in health should be carefully monitored, and comprehensive measures to alleviate health inequalities are needed, especially for young populations.

CERTAIN FRACTIONAL INTEGRAL INEQUALITIES ASSOCIATED WITH PATHWAY FRACTIONAL INTEGRAL OPERATORS

  • Agarwal, Praveen;Choi, Junesang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.1
    • /
    • pp.181-193
    • /
    • 2016
  • During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

SCALARIZATION METHODS FOR MINTY-TYPE VECTOR VARIATIONAL INEQUALITIES

  • Lee, Byung-Soo
    • East Asian mathematical journal
    • /
    • v.26 no.3
    • /
    • pp.415-421
    • /
    • 2010
  • Many kinds of Minty's lemmas show that Minty-type variational inequality problems are very closely related to Stampacchia-type variational inequality problems. Particularly, Minty-type vector variational inequality problems are deeply connected with vector optimization problems. Liu et al. [10] considered vector variational inequalities for setvalued mappings by using scalarization approaches considered by Konnov [8]. Lee et al. [9] considered two kinds of Stampacchia-type vector variational inequalities by using four kinds of Stampacchia-type scalar variational inequalities and obtain the relations of the solution sets between the six variational inequalities, which are more generalized results than those considered in [10]. In this paper, the author considers the Minty-type case corresponding to the Stampacchia-type case considered in [9].

PERTURBED PROXIMAL POINT ALGORITHMS FOR GENERALIZED MIXED VARIATIONAL INEQUALITIES

  • Jeong, Jae-Ug
    • East Asian mathematical journal
    • /
    • v.18 no.1
    • /
    • pp.95-109
    • /
    • 2002
  • In this paper, we study a class of variational inequalities, which is called the generalized set-valued mixed variational inequality. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert spaces, we have established an existence theorem of solutions for generalized set-valued mixed variational inequalities, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized set-valued mixed variational inequalities.

  • PDF

AUXILIARY PRINCEPLE AND ERROR ESTIMATES FOR VARIATIONAL INEQUALITIES

  • NOOR, MUHAMMED ASLAM
    • Honam Mathematical Journal
    • /
    • v.15 no.1
    • /
    • pp.105-120
    • /
    • 1993
  • The auxiliary principle technique is used to prove the uniqueness and the existence of solutions for a class of nonlinear variational inequalities and suggest an innovative iterative algorithm for computing the approximate solution of variational inequalities. Error estimates for the finite element approximation of the solution of variational inequalities are derived, which refine the previous known results. An example is given to illustrate the applications of the results obtained. Several special cases are considered and studied.

  • PDF