On real fixed points of one parameter family of Function x/${(b^{x}-1)}$

Abstract

In the present paper, the real fixed points of one parameter family ${\cal T}=\{f_{\lambda}(x)$$=\lambda\frac{x}{b^{x}-1}\; \text{and}\;f_{\lambda}(0)=\frac{\lambda}{\ln b} : \lambda>0, x \in \mathbb{R},b>0, b\neq 1\}$ are investigated. Further, the nature of these fixed points of $f_{\lambda}(x)$ are shown for $b>0$ except $b=1$.