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Propozycja wyzwalania twórczości matematycznej studentów przy pomocy pewnej nierówności funkcyjnej

Edyta Fiduk; Stanisław Siudut — 2016

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

T. Szostok and Sz. Wąsowicz in (Szostok, Wąsowicz, 2011) studied the following functional inequality: $| F (y) - F (x) - (y - x) f (\frac{x + y}{2}) | \leq ε$ stemming from the Lagrange mean value theorem. They proved that the functon $f$ is affine, provided $f, F : ℝ \to ℝ$ satisfy the above inequality for all $x, y \in ℝ$ . The aim of our paper is to extend the results of (Szostok, Wąsowicz, 2011) to more general situations (for example, we change $ℝ$ to $ℂ$ or $ℍ)$ .

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