Rolewicz's Problem (Solved)

Summary: Find all even, nonnegative, and differentiable functions $f: {\mathbb R} \rightarrow {\mathbb R}$ satisfying the inequality $f(t) - f(s) - f'(s)(t-s) \geq f(t-s), \; t,s \in {\mathbb R}$. This problem is motivated by the study of S. Rolewicz of Fréchet $\Phi$-differentiability of real-valued mappings of a metric space $(X,d)$.

Classification: Primary, functional analysis; Secondary, integral and functional equations

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