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

Katedra Matematyki (RMS/RMS1)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

Abstrakt

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.

Język oryginału	angielski
Numer artykułu	152
Czasopismo	Symmetry
Tom	17
Numer wydania	2
Identyfikatory DOI	https://doi.org/10.3390/sym17020152
Status publikacji	Opublikowano - lut 2025

Obszary tematyczne ASJC Scopus

Informatyka (różne)
Chemia (różne)
Matematyka ogólna
Fizyka i astronomia (różne)

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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.",

keywords = "Hyers–Ulam stability, difference operator, difference property, generalized polynomial",

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doi = "10.3390/sym17020152",

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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

UR - https://www.scopus.com/pages/publications/85219050192

U2 - 10.3390/sym17020152

DO - 10.3390/sym17020152

M3 - Article

AN - SCOPUS:85219050192

SN - 2073-8994

VL - 17

JO - Symmetry

JF - Symmetry

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Stability of Fréchet Functional Equation in Class of Differentiable Functions

Abstrakt

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