Ulam Stability in Real Inner-Product Spaces

Authors : Bianca Mosnegutu, Alexandra Mǎdutǎ

Pages : 113-115

Doi:10.33205/cma.758854

View : 20 | Download : 14

Publication Date : 2020-09-14

Article Type : Research

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