Post-quantum trapezoid type inequalities

Latif M. A., Kunt M., Dragomir S. S., Iscan I.

AIMS MATHEMATICS, vol.5, no.4, pp.4011-4026, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3934/math.2020258
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4011-4026
  • Keywords: Hermite-Hadamard inequality, q-integral inequalities, (p, q)-integral inequalities, (p, q)-derivative, (p, q)-integration, convexity, quasi-convexity, MIDPOINT TYPE INEQUALITIES, INTEGRAL-INEQUALITIES, DIFFERENTIABLE MAPPINGS, CONVEX
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this study, the assumption of being differentiable for the convex function f in the (p, q)-Hermite-Hadamard inequality is removed. A new identity for the right-hand part of (p, q)-Hermite-Hadamard inequality is proved. By using established identity, some (p, q)-trapezoid integral inequalities for convex and quasi-convex functions are obtained. The presented results in this work extend some results from the earlier research.