The real fixed points of two-parameter family of functions

Abstract

In this paper, we delve into the investigation of real fixed points of a two-parameter family of functions defined as [Formula: see text] where [Formula: see text] and m is a natural number. Our focus is to study the real fixed points of [Formula: see text] 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 [Formula: see text] does not change for any odd or even value of m, provided [Formula: see text] In each case of m and [Formula: see text] we conclude that the family of functions [Formula: see text] has exactly one attracting fixed point, two indifferent fixed points, and more than two repelling fixed points.

Keywords

• Bifurcation
• fixed points
• orbit
• two-parameter functions
• 37C25
• 30D05