Different types of quantum integral inequalities via [Formula: see text] -convexity

Yao Zhang; Ting-Song Du; Hao Wang; Yan-Jun Shen

doi:10.1186/s13660-018-1860-2

Different types of quantum integral inequalities via $(α, m)$ -convexity

J Inequal Appl. 2018;2018(1):264. doi: 10.1186/s13660-018-1860-2. Epub 2018 Sep 27.

Authors

Yao Zhang¹, Ting-Song Du^{1

2}, Hao Wang¹, Yan-Jun Shen³

Affiliations

¹ 1Department of Mathematics, College of Science, China Three Gorges University, Yichang, China.
² 2Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China.
³ 3Hubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges University, Yichang, China.

Abstract

In this paper, based on $(α, m)$ -convexity, we establish different type inequalities via quantum integrals. These inequalities generalize some results given in the literature.

Keywords: ( α , m ) -convex functions; Hermite–Hadamard’s inequality; Quantum integral inequalities; Simpson’s inequality.