Convexity of Solutions for an Iterative Equation in Banach Spaces

Abstract EN

By applying Schauder's fixed point theorem we investigate the existence of increasing (decreasing) solutions of the iterative equation ℋf∘f=F and further give conditions under which those solutions are convex or concave.

As corollaries we obtain results on iterative equation Gfx,fn1,…,fnkx=F(x) in Banach spaces, where n1,n2,…,nk≥2.