q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
JOURNAL OF KING SAUD UNIVERSITY SCIENCE, cilt.30, sa.2, ss.193-203, 2018 (SCI-Expanded, Scopus)
- 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.