(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, cilt.112, ss.969-992, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 112 Konu: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s13398-017-0402-y
  • Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Sayfa Sayıları: ss.969-992

Özet

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.