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

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

Abstract 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 inequ...

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Bibliographic Details
Main Authors: Yi-Xia Li, Muhammad Aamir Ali, Hüseyin Budak, Mujahid Abbas, Yu-Ming Chu
Format: Article
Language:English
Published: SpringerOpen 2021-04-01
Series:Advances in Difference Equations
Subjects:
Hermite–Hadamard inequality
Trapezoid inequalities
Midpoint inequalities
Quantum calculus
Convex functions
Online Access:https://doi.org/10.1186/s13662-021-03382-0
Description
Summary:Abstract 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.
ISSN:1687-1847

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