Abstract :

In this paper, we delve into the investigation of real fixed points of a two-parameter family of functions defined as fα,m(x)=α(bx−1)xm, where x≠0,α≠0,b>0,b≠1, and m is a natural number. Our focus is to study the real fixed points of fα,m(x) and understand their nature. Throughout our analysis, we discover that the number of fixed points depends on the values of α and the parity of m. Furthermore, we find that the number of fixed points of fα,m does not change for any odd or even value of m, provided m>2. In each case of m and b, we conclude that the family of functions fα,m has exactly one attracting fixed point, two indifferent fixed points, and more than two repelling fixed points.