Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON A VARIANT OF JENSEN'S INEQUALITY FOR FUNCTIONS WITH NONDECREASING INCREMENTS

  • Bakula, Milica Klaricic (Department of Mathematics Faculty of Natural Sciences Mathematics and Education University of Split) ;
  • Matkovic, Anita (Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture University of Split) ;
  • Pecaric, Josip (Faculty of Textile Technology University of Zagreb)
  • Published : 2008.05.31
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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.

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References

  1. S. Abramovich, M. Klaricic Bakula, M. Matic, and J.Pecaric, A variant of Jensen-Steffensen's inequality and quasi-arithmetic means, J. Math. Anal. Appl. 307 (2005), no. 1, 370-386 https://doi.org/10.1016/j.jmaa.2004.10.027
  2. H. D. Brunk, Integral inequalities for functions with nondecreasing increments, Pacific J. Math. 14 (1964), 783-793 https://doi.org/10.2140/pjm.1964.14.783
  3. A. McD. Mercer, A variant of Jensen's inequality, J. Inequal. Pure Appl. Math. 4 (2003), no. 4, Article 73, 2 pp
  4. C. T. Ng, Functions generating Schur-convex sums, General inequalities, 5 (Oberwolfach, 1986), 433-438, Internat. Schriftenreihe Numer. Math., 80, Birkhauser, Basel, 1987
  5. J. E. Pecaric, On some inequalities for functions with nondecreasing increments, J. Math. Anal. Appl. 98 (1984), no. 1, 188-197 https://doi.org/10.1016/0022-247X(84)90287-7
  6. J. E. Pecaric, Generalization of some results of H. Burkill and L. Mirsky and some related results, Period. Math. Hungar. 15 (1984), no. 3, 241-247 https://doi.org/10.1007/BF02454173
  7. J. E. Pecaric, Some inequalities for generalized convex functions of several variables, Period. Math. Hungar. 22 (1991), no. 2, 83-90 https://doi.org/10.1007/BF02327862
  8. J. E. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992