SOME NEW INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE DERIVATIVES OF ABSOLUTE VALUES ARE CONVEX AND CONCAVE


ÖZDEMİR M. E., EKİNCİ A., AKDEMİR A. O.

TWMS Journal of Pure and Applied Mathematics, vol.2, no.10, pp.212-224, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2 Issue: 10
  • Publication Date: 2019
  • Journal Name: TWMS Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.212-224
  • Keywords: convex functions, concave functions, Hermite-Hadamard inequality, Power-Mean inequality
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we prove some new inequalities for the functions whose derivatives' absolute values are convex and concave by dividing the interval [a, b] to n + 1 equal even sub-intervals. We obtain some new results involving intermediate values of vertical bar f'vertical bar in [a, b] by using some classical inequalities like Hermite-Hadamard, Holder and Power-Mean.