GENERALIZATIONS OF INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE CONVEX AND m- CONVEX

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ÖZDEMİR M. E., Ekinci A., Akdemir A. O.

MISKOLC MATHEMATICAL NOTES, vol.13, no.2, pp.441-457, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.18514/mmn.2012.436
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.441-457
  • Keywords: convex functions, m-convex functions, Simpson's inequality, power mean inequality, HADAMARD TYPE
  • Bursa Uludag University Affiliated: No

Abstract

In this paper, we establish some new integral inequalities for convex and m-convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results.