A new generalization of some quantum integral inequalities for quantum differentiable convex functions

Advances in Difference Equations

Yi-Xia Li¹  Hüseyin Budak²  Mujahid Abbas³  Yu-Ming Chu⁴  Muhammad Aamir Ali⁵ 

[1] College of Mathematics and Finance, Xiangnan University, 423000, Chenzhou, P.R. China;Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey;Department of Mathematics, Government College University, 54000, Lahore, Pakistan;Department of Mathematics, Huzhou University, 313000, Huzhou, China;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China;

关键词: Hermite–Hadamard inequality;    Trapezoid inequalities;    Midpoint inequalities;    Quantum calculus;    Convex functions;    26D10;    26D15;    26A51;   

DOI  :  10.1186/s13662-021-03382-0

来源: Springer

【 摘 要 】

In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

【 授权许可】

CC BY