Ulam Stability in Real Inner-Product Spaces
Ulam Stability in Real Inner-Product Spaces
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,
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- 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.
- ISSN: 2651-2939
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Tuncer ACAR