The $G$-translativity of Abel-type Transformations

Abstract

Suppose $0<t_{n}<1$ and $\lim_{n\rightarrow\infty}$ $t_{n}=1$, then the Abel-type matrix, denoted by $A_{\alpha,t}$, is the matrix defined by
\[
a_{nk}=\left(\stackrel{k+\alpha}{k}\right)t^{k}_{n}\left(1-t_{n}\right)^{\alpha+1},\quad\alpha>-1.
\]
Recently the author proved that the Abel-type matrix $A_{\alpha,t}$ is $\ell$-transla\-ti\-ve [2]. In this paper, we investigate the $G$-translativity of these transformations.

2000 Mathematics Subject Classification. 40A05, 40D99, 40C05