Displaying similar documents to “On the stability of the functional equation of the first order”

On the inverse stability of functional equations

Zenon Moszner (2013)

Banach Center Publications

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The inverse stability of functional equations is considered, i.e. when the function, approximating a solution of the equation, is an approximate solution of this equation.

Stability of a generalization of the Fréchet functional equation

Renata Malejki (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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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.

On the stability of the squares of some functional equations

Zenon Moszner (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of the equation of isometry.

On the Stability of Orthogonal Additivity

Włodzimierz Fechner, Justyna Sikorska (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.