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Regular fractional iteration of convex functions

Marek Kuczma — 1980

Annales Polonici Mathematici

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.

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