# Search results for: Renata Malejki

Aequationes mathematicae > 2018 > 92 > 2 > 355-373

Journal of Mathematical Analysis and Applications > 2016 > 442 > 2 > 537-553

Commentationes Mathematicae > 2014 > 54 > 1

Aequationes mathematicae > 2018 > 92 > 2 > 355-373

We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation...

Journal of Mathematical Analysis and Applications > 2016 > 442 > 2 > 537-553

We prove some general stability and hyperstability results for a generalization of the well known Fréchet equation, stemming from the characterization of the inner product spaces due to Jordan and von Neumann. The main result yields several stability outcomes for various other well known functional equations. Thus we obtain in particular some new inequalities characterizing the inner product spaces...

We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.

Commentationes Mathematicae > 2014 > 54 > 1

In this paper we will study some approximate properties of Baskakov-Durrmeyer type operators \(M_n^{\alpha,a}\). We determine the rate of convergence and prove the Voronovskaya type theorem for those operators.