Ulam Stability in Real Inner-Product Spaces

Yıl 2020, , 113 - 115, 14.09.2020

Bianca Mosnegutu , Alexandra Mǎdutǎ

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

Cited By: 2

Öz

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.

Anahtar Kelimeler

Ulam stability, Ortogonality equation, Gram equation

Kaynakça

• J. Brzde¸k, D. Popa, I. Ra¸sa and Xu. B: Ulam stability of operators, Academic Press, London(2018).
• D. S. Marinescu, M. Monea and C. Mortici: Some characterizations of inner product spaces via some geometrical inequalities, Appl. Anal. Discrete Math., 11 (2017), 424-433.
• N. Minculete: Considerations about the several inequalities in an inner product space, Math. Inequalities, 1 (2018), 155– 161.
• S. M. S. Nabavi: On mappings which approximately preserve angles, Aequationes Math. 92 (2018), 1079–1090.
• D. Popa and I. Ra¸sa: Inequalities involving the inner product. JIPAM, 8 (3) (2007), Article 86.