Convexity according to a pair of quasi-arithmetic means and inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:488

Article

Dinh Thanh Duc¹  Nguyen Ngoc Hue²  Nguyen Du Vi Nhan^1,3  Vu Kim Tuan⁴ 

[1] Quy Nhon Univ, Dept Math & Stat, Binh Dinh, Vietnam

[2] Tay Nguyen Univ, Dept Nat Sci & Technol, Daklak, Vietnam

[3] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[4] Univ West Georgia, Dept Math, Carrollton, GA 30118 USA

关键词: Quasi-arithmetic mean;    Convexity;    Hermite-Hadamard inequality;    Fejer inequality;    Fractional integral;    Gamma function;   

DOI  :  10.1016/j.jmaa.2020.124059

来源: Elsevier

【 摘 要 】

We consider a class of generalized convex functions, which are defined according to a pair of quasi-arithmetic means and called (M-phi, M-psi)-convex functions, and establish various Fejer type inequalities for such a function class. These inequalities not merely provide a natural and intrinsic characterization of the (M-phi, M-psi)-convex functions, but actually offer a generalization and refinement of the most part of the concrete Hermite-Hadamard and Fejer type inequalities obtained in earlier studies for different kinds of convexity and fractional integrals. Applications to inequalities involving the gamma function and special means are also included. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free