q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions


Alp N., SARIKAYA M. Z. , KUNT M. , İŞCAN İ.

JOURNAL OF KING SAUD UNIVERSITY SCIENCE, vol.30, no.2, pp.193-203, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jksus.2016.09.007
  • Title of Journal : JOURNAL OF KING SAUD UNIVERSITY SCIENCE
  • Page Numbers: pp.193-203
  • Keywords: Hermite-Hadamard inequality, Midpoint type inequality, q-Integral inequalities, q-Derivative, q-Integration, Convexity, Quasi-convexity, INTEGRAL-INEQUALITIES

Abstract

In this paper, we prove the correct q-Hermite-Hadamard inequality, some new q-Hermite-Hadamard inequalities, and generalized q-Hermite-Hadamard inequality. By using the left hand part of the correct q-Hermite-Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works. (C) 2016 The Authors. Production and hosting by Elsevier B.V.