On Extended Convex Functions via Incomplete Gamma Functions. (31st July 2021)

• Record Type: Journal Article
• Authors: Zhao, Yan; Saleem, M. Shoaib; Mehmood, Shahid; Salleh, Zabidin
• Other Names: Yalçın Sibel Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-07-31
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/1924242
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h -exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He's inequalities for h -exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature.