Generalized orthogonality equations in finite-dimensional normed spaces

被引：1
|
作者：
Gryszka, Karol [1 ]
Wojcik, Pawel [1 ]
机构：
[1] Pedag Univ Krakow, Inst Math, Podchorazych 2, PL-30084 Krakow, Poland
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2023年 / 14卷 / 02期
关键词：
Functional equations; Normed space; Norm derivatives; Orthogonal equation; Smoothness; Rotundity; BANACH-SPACES; FUNCTIONAL-EQUATION;
D O I：
10.1007/s43034-023-00264-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X, Y be real normed spaces and let p '(+), p '(-) be norm derivatives. In this work, we solve a system of functional equations{p '(+)( f(x), f(y)) = g(x)p '(+)(x, y),p '(-)( f (x), f (y)) = g(x)p '(-)(x, y),with unknown functions f : X -> Y, g : X -> R. Moreover, we give partial answer to open problem posed in 2010.
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页数：13
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