Q-Hermite–Hadamard Inequalities for Generalized Exponentially s, m;η-Preinvex Functions. (19th April 2021)

• Record Type: Journal Article
• Authors: Wang, Hua; Kalsoom, Humaira; Budak, Hüseyin; Idrees, Muhammad
• Other Names: Akdemir Ahmet Ocak Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-04-19
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5577340
• Languages: English
• ISSNs: 2314-4629

Abstract

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