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A proof of S. Rolewicz’s conjecture. (English) Zbl 1156.26304
Summary: S. Rolewicz’s conjecture concerning solutions of the functional-differential inequality
$f(t)-f(s)-f'(s)(t-s)\geq f(t-s), \quad t,s\in\mathbb R, \tag{P}$
is proved.

##### MSC:
 26D10 Inequalities involving derivatives and differential and integral operators 39B62 Functional inequalities, including subadditivity, convexity, etc. 34A40 Differential inequalities involving functions of a single real variable 52A01 Axiomatic and generalized convexity