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
  • 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.