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Keywords = (q, ω)-Hahn difference operator

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10 pages, 794 KiB  
Article
Ostrowski–Trapezoid–Grüss-Type on (q, ω)-Hahn Difference Operator
by Ahmed A. El-Deeb and Jan Awrejcewicz
Symmetry 2022, 14(9), 1776; https://doi.org/10.3390/sym14091776 - 26 Aug 2022
Cited by 7 | Viewed by 1593
Abstract
We use two parameters for functions whose second (q, ω)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (q, ω)-Hahn difference operator. Furthermore, we procure some q [...] Read more.
We use two parameters for functions whose second (q, ω)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (q, ω)-Hahn difference operator. Furthermore, we procure some q-integral and continuous inequalities as special cases of the main results as well these generalizations. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article
(This article belongs to the Section Mathematics)
16 pages, 330 KiB  
Article
Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem
by Rujira Ouncharoen, Nichaphat Patanarapeelert and Thanin Sitthiwirattham
Symmetry 2021, 13(11), 2174; https://doi.org/10.3390/sym13112174 - 12 Nov 2021
Viewed by 1443
Abstract
The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a [...] Read more.
The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results. Full article
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