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Solution and stability of an n-dimensional functional equation

  • Sandra Pinelas ORCID logo EMAIL logo , V. Govindan and K. Tamilvanan
Published/Copyright: September 18, 2019

Abstract

In this paper, we prove the general solution and generalized Hyers–Ulam stability of n-dimensional functional equations of the form

i=1ijknf(-xi-xj-xk+l=1lijknxl)=(n3-9n2+20n-126)i=1nf(xi),

where n is a fixed positive integer with -{0,1,2,3,4}, in a Banach space via direct and fixed point methods.

Award Identifier / Grant number: 02.a03.21.0008

Funding statement: The publication was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008).

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Received: 2018-05-04
Revised: 2019-02-04
Accepted: 2019-09-04
Published Online: 2019-09-18
Published in Print: 2019-10-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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