The Newton's method that I know is defined as follows:

$$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$

However, I've recently encountered a paper that talks about a ** one-parameter family of Newton's method** (page 4, equation 2.8), defined as follows:

$$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)-pf(x_n)}$$

What is this $p$ parameter in the equation above? Why is it not present in the first equation? What is this parameter useful for? What is that *one-parameter* Newton's method?