(p, q)-Hermite-Hadamard inequalities and (p, q)-estimates for midpoint type inequalities via convex and quasi-convex functions

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

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.112, no.4, pp.969-992, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 112 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s13398-017-0402-y
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.969-992
  • Keywords: Hermite-Hadamard inequality, Midpoint type inequality, q-integral inequalities, (p, q)-integral inequalities, (p, q)-derivative, (p, q)-integration, Convexity, Quasi-convexity, HERMITE-HADAMARD INEQUALITIES, INTEGRAL-INEQUALITIES
  • Karadeniz Technical University Affiliated: Yes

Abstract

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