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On Hosszú’s functional inequality. (English) Zbl 0697.39014
The authors prove that every continuous and concave function f: (0,1)$$\to {\mathbb{R}}$$ satisfies Hosszu’s inequality $(1)\quad f(x+y-xy)+f(xy)\leq f(x)+f(y).$ Moreover, if $$a\in [23/16,3/2)$$, then the function f defined on (0,1) by $$f(x)=-x^ 4+2x^ 3-ax^ 2$$ is a continuous solution of (1) and f is not concave.
Reviewer: M.C.Zdun

##### MSC:
 39B72 Systems of functional equations and inequalities