Leibniz’s Rule and Fubini’s Theorem Associated with a General Quantum Difference Operator

2020 ◽  
pp. 121-134
Author(s):  
Alaa E. Hamza ◽  
Enas M. Shehata ◽  
Praveen Agarwal
Keyword(s):  
Difference Operator ◽  
Fubini’S Theorem ◽  
General Quantum ◽  
Quantum Difference ◽  
Fubini's Theorem

scholarly journals A general quantum Laplace transform

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Enas M. Shehata ◽  
Nashat Faried ◽  
Rasha M. El Zafarani
Keyword(s):  
Continuous Function ◽  
Laplace Transform ◽  
Difference Equations ◽  
Difference Operator ◽  
General Quantum ◽  
Quantum Difference

Abstract In this paper, we introduce a general quantum Laplace transform $\mathcal{L}_{\beta }$ L β and some of its properties associated with the general quantum difference operator ${D}_{\beta }f(t)= ({f(\beta (t))-f(t)} )/ ({ \beta (t)-t} )$ D β f ( t ) = ( f ( β ( t ) ) − f ( t ) ) / ( β ( t ) − t ) , β is a strictly increasing continuous function. In addition, we compute the β-Laplace transform of some fundamental functions. As application we solve some β-difference equations using the β-Laplace transform. Finally, we present the inverse β-Laplace transform $\mathcal{L}_{\beta }^{-1}$ L β − 1 .

scholarly journals Leibnizs rule and Fubinis theorem associated with Hahn difference operators

2016 ◽  
Vol 12 (6) ◽  
pp. 6335-6346 ◽  
Author(s):  
Samer Derham Makarash
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Fubini’S Theorem ◽  
Hahn Difference Operator ◽  
Fubini's Theorem

In $1945$, Wolfgang Hahn introduced his difference operator $D_{q,\omega}$, which is defined by where $\displaystyle{\omega_0=\frac {\omega}{1-q}}$ with $0<q<1, \omega>0.$ In this paper, we establish Leibniz's rule and Fubini's theorem associated with this Hahn difference operator.

scholarly journals On the application of Fubini's theorem in the integration of functiions of two variables in a measure space

2013 ◽  
Vol 1 (2) ◽  
Author(s):  
'Bankole V Akinremi ◽  
Ubong Sam Idiong ◽  
Bridjet Akintewe ◽  
Kayode Samuel Famuagun
Keyword(s):  
Measure Space ◽  
Fubini’S Theorem ◽  
Fubini's Theorem

scholarly journals Fubini’s Theorem for Non-Negative or Non-Positive Functions

2018 ◽  
Vol 26 (1) ◽  
pp. 49-67
Author(s):  
Noboru Endou
Keyword(s):  
Integrable Function ◽  
Functional Space ◽  
The Other ◽  
Integration Theory ◽  
Fubini’S Theorem ◽  
Positive Functions ◽  
System 1 ◽  
Article 5 ◽  
Fubini's Theorem ◽  
Lebesgue Integration

Summary The goal of this article is to show Fubini’s theorem for non-negative or non-positive measurable functions [10], [2], [3], using the Mizar system [1], [9]. We formalized Fubini’s theorem in our previous article [5], but in that case we showed the Fubini’s theorem for measurable sets and it was not enough as the integral does not appear explicitly. On the other hand, the theorems obtained in this paper are more general and it can be easily extended to a general integrable function. Furthermore, it also can be easy to extend to functional space Lp [12]. It should be mentioned also that Hölzl and Heller [11] have introduced the Lebesgue integration theory in Isabelle/HOL and have proved Fubini’s theorem there.

The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem

2004 ◽  
Vol 111 (4) ◽  
pp. 340-347
Author(s):  
Asuman Aksoy ◽  
Mario Martelli
Keyword(s):  
Wave Equation ◽  
Partial Derivatives ◽  
Fubini’S Theorem ◽  
Fubini's Theorem
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