文章基本信息

标题：A general quantum difference calculus
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作者：Alaa E Hamza ; Abdel-Shakoor M Sarhan ; Enas M Shehata 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：182
DOI：10.1186/s13662-015-0518-3
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we consider a strictly increasing continuous function β, and we present a general quantum difference operator D β $D_{\beta}$ which is defined to be D β f ( t ) = ( f ( β ( t ) ) − f ( t ) ) / ( β ( t ) − t ) ${D}_{\beta}f(t)= ({f(\beta(t))-f(t)} )/ ({\beta(t)-t} )$ . This operator yields the Hahn difference operator when β ( t ) = q t + ω $\beta(t)=qt+\omega$ , the Jackson q-difference operator when β ( t ) = q t $\beta (t)=qt$ , q ∈ ( 0 , 1 ) $q\in(0,1)$ , ω > 0 $\omega>0$ are fixed real numbers and the forward difference operator when β ( t ) = t + ω $\beta(t)=t+\omega$ , ω > 0 $\omega>($ . A calculus based on the operator D β $D_{\beta}$ and its inverse is established.
关键词：quantum difference operator ; quantum calculus ; Hahn difference operator ; Jackson q -difference operator