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, cilt.30, ss.193-203, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30 Konu: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jksus.2016.09.007
  • Dergi Adı: JOURNAL OF KING SAUD UNIVERSITY SCIENCE
  • Sayfa Sayıları: ss.193-203

Özet

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.