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On a variant of Jensen's inequality for functions with nondecreasing increments

Josip Pecaric|Milica Klaricic Bakula|Anita Matkovic
대한수학회 (The Korean Mathematical Society)|2008.05|대한수학회지 (Journal of the KMS)|제45권 제3호|pp. 821-834

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참고문헌

키워드

Jensen’s inequalityHolder’s inequalityfunctions with nondecreasing incrementsCebysev’s inequality
주제분류수학

초록

Refinements of a variant of Jensen’s inequality for functions with nondecreasing increments are presented. Obtained results are used to prove refinements of related variants of Cebysev’s inequality and Holder’s inequality.

Abstract

Refinements of a variant of Jensen’s inequality for functions with nondecreasing increments are presented. Obtained results are used to prove refinements of related variants of Cebysev’s inequality and Holder’s inequality.

참고문헌 (8)

  1. S. Abramovich, "A variant of Jensen-Steffensen’s inequality and quasi-arithmetic means", Journal of Mathematical Analysis and Applications, 307(1), pp.370~386 (2005)
  2. H. D. Brunk, "Integral inequalities for functions with nondecreasing increments", Pacific Journal of Mathematics, 14, pp.783~793 (1964)
  3. A. McD. Mercer, "A variant of Jensen’s inequality", Journal of Inequalities in Pure and Applied Mathematics, 4(4), pp.2~ (2003)
  4. C. T. Ng, "Functions generating Schur-convex sums, General inequalities, 5 (Oberwolfach, 1986)", International Series of Numerical Mathematics, 80, pp.433~438 (1987)
  5. J. E. Pecaric, "On some inequalities for functions with nondecreasing increments", Journal of Mathematical Analysis and Applications, 98(1), pp.188~197 (1984)
  6. J. E. Pecaric, "Generalization of some results of H. Burkill and L. Mirsky and some related results", Periodica Mathematica Hungarica, 15(3), pp.241~247 (1984)
  7. J. E. Pecaric, "Some inequalities for generalized convex functions of several variables", Periodica Mathematica Hungarica, 22(2), pp.83~90 (1991)
  8. J. E. Pecaric, "Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering", pp.187~ (1992), Academic Press, Inc.

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