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## Ulam Stability in Real Inner-Product Spaces

#### Bianca MOSNEGUTU [1] , Alexandra MǍDUTǍ [2]

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.

Ulam stability, Ortogonality equation, Gram equation
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Primary Language en Mathematics Articles Author: Bianca MOSNEGUTU (Primary Author)Institution: Technical University of Cluj-NapocaCountry: Romania Author: Alexandra MǍDUTǍ Institution: TECHNICAL UNIVERSITY OF CLUJ-NAPOCACountry: Romania Publication Date : September 14, 2020
 Bibtex @research article { cma758854, journal = {Constructive Mathematical Analysis}, issn = {2651-2939}, address = {}, publisher = {Tuncer ACAR}, year = {2020}, volume = {3}, pages = {113 - 115}, doi = {10.33205/cma.758854}, title = {Ulam Stability in Real Inner-Product Spaces}, key = {cite}, author = {Mosnegutu, Bianca and Mǎdutǎ, Alexandra} } APA Mosnegutu, B , Mǎdutǎ, A . (2020). Ulam Stability in Real Inner-Product Spaces . Constructive Mathematical Analysis , 3 (3) , 113-115 . DOI: 10.33205/cma.758854 MLA Mosnegutu, B , Mǎdutǎ, A . "Ulam Stability in Real Inner-Product Spaces" . Constructive Mathematical Analysis 3 (2020 ): 113-115 Chicago Mosnegutu, B , Mǎdutǎ, A . "Ulam Stability in Real Inner-Product Spaces". Constructive Mathematical Analysis 3 (2020 ): 113-115 RIS TY - JOUR T1 - Ulam Stability in Real Inner-Product Spaces AU - Bianca Mosnegutu , Alexandra Mǎdutǎ Y1 - 2020 PY - 2020 N1 - doi: 10.33205/cma.758854 DO - 10.33205/cma.758854 T2 - Constructive Mathematical Analysis JF - Journal JO - JOR SP - 113 EP - 115 VL - 3 IS - 3 SN - 2651-2939- M3 - doi: 10.33205/cma.758854 UR - https://doi.org/10.33205/cma.758854 Y2 - 2020 ER - EndNote %0 Constructive Mathematical Analysis Ulam Stability in Real Inner-Product Spaces %A Bianca Mosnegutu , Alexandra Mǎdutǎ %T Ulam Stability in Real Inner-Product Spaces %D 2020 %J Constructive Mathematical Analysis %P 2651-2939- %V 3 %N 3 %R doi: 10.33205/cma.758854 %U 10.33205/cma.758854 ISNAD Mosnegutu, Bianca , Mǎdutǎ, Alexandra . "Ulam Stability in Real Inner-Product Spaces". Constructive Mathematical Analysis 3 / 3 (September 2020): 113-115 . https://doi.org/10.33205/cma.758854 AMA Mosnegutu B , Mǎdutǎ A . Ulam Stability in Real Inner-Product Spaces. CMA. 2020; 3(3): 113-115. Vancouver Mosnegutu B , Mǎdutǎ A . Ulam Stability in Real Inner-Product Spaces. Constructive Mathematical Analysis. 2020; 3(3): 113-115. IEEE B. Mosnegutu and A. Mǎdutǎ , "Ulam Stability in Real Inner-Product Spaces", Constructive Mathematical Analysis, vol. 3, no. 3, pp. 113-115, Sep. 2020, doi:10.33205/cma.758854

Authors of the Article
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