Regular fractional iteration of convex functions

Marek Kuczma. "Regular fractional iteration of convex functions." Annales Polonici Mathematici 38.1 (1980): 95-100. <http://eudml.org/doc/265331>.

@article{MarekKuczma1980,
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.},
author = {Marek Kuczma},
journal = {Annales Polonici Mathematici},
keywords = {fractional iteration; convex functions; Schröder equation; Abel equation; continuous solution},
language = {eng},
number = {1},
pages = {95-100},
title = {Regular fractional iteration of convex functions},
url = {http://eudml.org/doc/265331},
volume = {38},
year = {1980},
}

TY - JOUR
AU - Marek Kuczma
TI - Regular fractional iteration of convex functions
JO - Annales Polonici Mathematici
PY - 1980
VL - 38
IS - 1
SP - 95
EP - 100
AB - 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.
LA - eng
KW - fractional iteration; convex functions; Schröder equation; Abel equation; continuous solution
UR - http://eudml.org/doc/265331
ER -