We present a complete theory for the stability of non-hyperbolic fixed points of one-dimensional continuous maps. As well as we give simple criteria for the global stability of general maps without using derivatives.
Taylor & Francis
Dannan, F.M., Elaydi, S.N., & Ponomarenko, V. (2003). Stability of hyperbolic and nonhyperbolic fixed points of one-dimensional maps. Journal of Difference Equations and Applications, 9(5), 449-457. doi:10.1080/1023619031000078315
Journal of Difference Equations and Applications