Problem #PRU-109819

Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Monotonicity, boundedness

14–16 4.0

Problem

Is there a bounded function $f : R \to R$ such that $f (1) > 0$ and $f (x)$ satisfies the inequality $f^{2} (x + y) \geq f^{2} (x) + 2 f (x y) + f^{2} (y)$ for all $x, y \in R$ ?

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