Generalized orthogonality equations in finite-dimensional normed spaces

Autor: Karol Gryszka, Paweł Wójcik
Rok vydání: 2023
Předmět:
Zdroj: Annals of Functional Analysis. 14
ISSN: 2008-8752
2639-7390
DOI: 10.1007/s43034-023-00264-2
Popis: Let X, Y be real normed spaces and let $$\rho '_+$$ ρ + ′ , $$\rho '_-$$ ρ - ′ be norm derivatives. In this work, we solve a system of functional equations $$\begin{aligned} {\left\{ \begin{array}{ll}\rho '_+(f(x),f(y))=g(x)\rho '_+(x,y),\\ \rho '_-(f(x),f(y))=g(x)\rho '_-(x,y), \end{array}\right. } \end{aligned}$$ ρ + ′ ( f ( x ) , f ( y ) ) = g ( x ) ρ + ′ ( x , y ) , ρ - ′ ( f ( x ) , f ( y ) ) = g ( x ) ρ - ′ ( x , y ) , with unknown functions $$f:X\!\rightarrow \!Y$$ f : X → Y , $$g:X\rightarrow \mathbb {R}$$ g : X → R . Moreover, we give partial answer to open problem posed in 2010.
Databáze: OpenAIRE
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