Nowhere coexpanding functions
This work addresses a theoretical problem in mathematical analysis for researchers studying dynamical systems and function properties, but it appears incremental as it builds on existing results like Singer's theorem.
The paper tackles the problem of analyzing fixed points for a newly defined family of C^1 functions called 'nowhere coexpanding functions', which are closed under composition and include C^3 functions with non-positive Schwarzian derivative, and it generalizes a classic result by Singer on the nature of these fixed points.
We define a family of $C^1$ functions which we call "nowhere coexpanding functions" that is closed under composition and includes all $C^3$ functions with non-positive Schwarzian derivative. We establish results on the number and nature of the fixed points of these functions, including a generalisation of a classic result of Singer.