Regular fractional iteration of convex functions
Volume 38 / 1980
Annales Polonici Mathematici 38 (1980), 95-100
DOI: 10.4064/ap-38-1-95-100
Abstract
The existence of a unique $C^1$ solution φ of equation (1) is proved under the condition that f: I → I is convex or concave and of class $C^1$ in I, 0 < f(x) < x in I*, and f'(x) > 0 in I. Here I = [0, a] or [0, a), 0 < a ≤ ∞, and I* = I\ {0}.
