Ulam Stability in Real Inner-Product Spaces

Year 2020, Volume: 3 Issue: 3, 113 - 115, 14.09.2020

Bianca Mosnegutu , Alexandra Mǎdutǎ

https://doi.org/10.33205/cma.758854

Cited By: 2

Abstract

Roughly speaking an equation is called Ulam stable if near each approximate solution of the equation
there exists an exact solution. In this paper we prove that Cauchy-Schwarz equation, Ortogonality equation and Gram
equation are Ulam stable.

This paper is concerned with the Ulam stability of some classical equations arising in thecontext of inner-product spaces. For the general notion of Ulam stability see, e.q., [1]. Roughlyspeaking an equation is called Ulam stable if near every approximate solution there exists anexact solution; the precise meaning in each case presented in this paper is described in threetheorems. Related results can be found in [2, 3, 4]. See also [5] for some inequalities in innerproduct spaces.

Keywords

Ulam stability, Ortogonality equation, Gram equation

References

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