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Keywords = Qi type integral inequality

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11 pages, 263 KiB  
Article
Some New Anderson Type h and q Integral Inequalities in Quantum Calculus
by Munawwar Ali Abbas, Li Chen, Asif R. Khan, Ghulam Muhammad, Bo Sun, Sadaqat Hussain, Javed Hussain and Adeeb Ur Rasool
Symmetry 2022, 14(7), 1294; https://doi.org/10.3390/sym14071294 - 22 Jun 2022
Cited by 2 | Viewed by 2109
Abstract
The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of [...] Read more.
The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of mathematics that has been gaining considerable attention recently. Despite the fact of its application in discrete calculus, it can be applied in fractional calculus as well. In this paper, some new Anderson type q-integral and h-integral inequalities are given using a Feng Qi integral inequality in quantum calculus. These findings are highly beneficial for basic frontier theories, and the techniques offered by technology are extremely useful for those who can stimulate research interest in exploring mathematical applications. Due to the interesting properties in the field of mathematics, integral inequalities have a tied correlation with symmetric convex and convex functions. There exist strong correlations and expansive properties between the different fields of convexity and symmetric function, including probability theory, convex functions, and the geometry of convex functions on convex sets. The main advantage of these essential inequalities is that they can be converted into time-scale calculus. This kind of inevitable inequality can be very helpful in various fields where coordination plays an important role. Full article
(This article belongs to the Special Issue Symmetry in Quantum Calculus)
24 pages, 336 KiB  
Article
Qi Type Diamond-Alpha Integral Inequalities
by Zhong-Xuan Mao, Ya-Ru Zhu, Bao-Hua Guo, Fu-Hai Wang, Yu-Hua Yang and Hai-Qing Zhao
Mathematics 2021, 9(4), 449; https://doi.org/10.3390/math9040449 - 23 Feb 2021
Cited by 3 | Viewed by 2181
Abstract
In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales. Full article
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