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Two remarks on Hosszú’s functional inequality. (English) Zbl 0760.39005
The paper deals with the inequality (1) \(f(x+y-xy)+f(xy)\leq f(x)+f(y)\) which, according to [Gy. Maksa and Zs. Pales, Publ. Math. 36, No. 1-4, 187-189 (1989; Zbl 0697.39014)] is satisfied by concave functions but has also some continuous, non concave solutions. The author generalizes the result proving that (1) is satisfied by Wright-concave real functions defined in \((0,1)\) and satisfying (1). Also, (1) is satisfied by real functions with nonincreasing increments, defined in \((0,1)^ k\).
MSC:
39B72 Systems of functional equations and inequalities
26A51 Convexity of real functions in one variable, generalizations
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