Stability of Fréchet Functional Equation in Class of Differentiable Functions

Marcin Adam

doi:10.3390/sym17020152

Stability of Fréchet Functional Equation in Class of Differentiable Functions

Marcin Adam

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

Abstract

The goal of this work is to demonstrate the stability of the Fréchet functional equation in the class of differentiable functions with respect to a large class of seminorms defined by means of derivatives. To achieve this, I utilize previous results concerning the difference property of higher orders of the class of n-times continuously differentiable functions.

Original language	English
Article number	152
Journal	Symmetry
Volume	17
Issue number	2
DOIs	https://doi.org/10.3390/sym17020152
Publication status	Published - Feb 2025

Keywords

Hyers–Ulam stability
difference operator
difference property
generalized polynomial

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/sym17020152

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title = "Stability of Fr{\'e}chet Functional Equation in Class of Differentiable Functions",

abstract = "The goal of this work is to demonstrate the stability of the Fr{\'e}chet functional equation in the class of differentiable functions with respect to a large class of seminorms defined by means of derivatives. To achieve this, I utilize previous results concerning the difference property of higher orders of the class of n-times continuously differentiable functions.",

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AB - The goal of this work is to demonstrate the stability of the Fréchet functional equation in the class of differentiable functions with respect to a large class of seminorms defined by means of derivatives. To achieve this, I utilize previous results concerning the difference property of higher orders of the class of n-times continuously differentiable functions.

KW - Hyers–Ulam stability

KW - difference operator

KW - difference property

KW - generalized polynomial

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U2 - 10.3390/sym17020152

DO - 10.3390/sym17020152

M3 - Article

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SN - 2073-8994

VL - 17

JO - Symmetry

JF - Symmetry

IS - 2

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ER -

Stability of Fréchet Functional Equation in Class of Differentiable Functions

Abstract

Keywords

ASJC Scopus subject areas

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