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

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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.

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