Leibnizs rule and Fubinis theorem associated with Hahn difference operators

Samer Derham Makarash

doi:10.24297/jam.v12i6.3836

Abstract

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.

Highlights

In this paper, we establish Leibniz’s rule and Fubini’s theorem associated with this Hahn difference operator
We prove Fubini’s theorem in Hahn difference operator setting, that is, we prove that the iterated integrals are equal
In the folloing we present some needed results from [1] concerning the calculus associated with Dq

Summary

Introduction

We establish Leibniz’s rule and Fubini’s theorem associated with this Hahn difference operator. This paper is devoted to establishing Leibniz’s rule and Fubini’s theorem associated with the q, - difference operator. We prove Fubini’s theorem in Hahn difference operator setting, that is, we prove that the iterated integrals are equal.

Results

Conclusion