<i>q</i>-Hermite-Hadamard Inequalities for Generalized Exponentially (<i>s</i>, <i>m</i>; η)-Preinvex Functions

Wang H., Kalsoom H., Budak H., Idrees M.

JOURNAL OF MATHEMATICS, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1155/2021/5577340
  • Dergi Adı: JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this article, we introduce a new extension of classical convexity which is called generalized exponentially (s, m; eta)-preinvex functions. Also, it is seen that the new definition of generalized exponentially (s, m; eta)-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new (m kappa 2)q-integral identity for the twice (m kappa 2)q-differentiable function. By using this identity, we show essential new results for Hermite-Hadamard-type inequalities for the (m kappa 2)q-integral by utilizing differentiable exponentially (s, m; eta)-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.