Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second \(q^{b}\) -derivatives

Advances in Difference Equations

article

Ali, Muhammad Aamir¹  Budak, Hüseyin²  Abbas, Mujahid³  Chu, Yu-Ming⁴ 

[1] Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University;Department of Mathematics, Faculty of Science and Arts, Düzce University;Department of Mathematics, Government College University;Department of Mathematics, Huzhou University

关键词: Hermite–Hadamard inequality;    q -integral;    Quantum calculus;    Convex function;   

DOI  :  10.1186/s13662-020-03163-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of$q^{b}$ -integral. We prove some new inequalities related with right-hand sides of$q^{b}$ -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

【 授权许可】

CC BY