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, sa.2, ss.193-203, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jksus.2016.09.007
  • Dergi Adı: JOURNAL OF KING SAUD UNIVERSITY SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.193-203
  • Anahtar Kelimeler: Hermite-Hadamard inequality, Midpoint type inequality, q-Integral inequalities, q-Derivative, q-Integration, Convexity, Quasi-convexity, INTEGRAL-INEQUALITIES
  • Karadeniz Teknik Üniversitesi Adresli: Evet

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.