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.

引用

页数：13

共 50 条

[1] Generalized orthogonality equations in finite-dimensional normed spaces
Karol Gryszka
Paweł Wójcik
Annals of Functional Analysis, 2023, 14
[2] Approximate isometries on finite-dimensional normed spaces
Dilworth, SJ
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1999, 31 : 471 - 476
[3] The horofunction boundary of finite-dimensional normed spaces
Walsh, Cormac
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2007, 142 : 497 - 507
[4] On finite-dimensional normed spaces over Cp
Kubzdela, A
Ultrametric Functional Analysis, 2005, 384 : 169 - 185
[5] RESULTS ON AUERBACH BASES FOR FINITE-DIMENSIONAL NORMED SPACES
KNOWLES, RJ
COOK, TA
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (07): : A660 - A660
[6] The Local Steiner Problem in Finite-Dimensional Normed Spaces
Konrad J. Swanepoel
Discrete & Computational Geometry, 2007, 37 : 419 - 442
[7] Quotients of finite-dimensional quasi-normed spaces
Kalton, NJ
Litvak, AE
HOUSTON JOURNAL OF MATHEMATICS, 2002, 28 (03): : 585 - 598
[8] SYMMETRIC BLOCK BASES IN FINITE-DIMENSIONAL NORMED SPACES
GOWERS, WT
ISRAEL JOURNAL OF MATHEMATICS, 1989, 68 (02) : 193 - 219
[9] The local Steiner problem in finite-dimensional normed spaces
Swanepoel, Konrad J.
DISCRETE & COMPUTATIONAL GEOMETRY, 2007, 37 (03) : 419 - 442
[10] BODIES OF CONSTANT WIDTH IN FINITE-DIMENSIONAL NORMED SPACES
SOLTAN, VP
MATHEMATICAL NOTES, 1979, 25 (1-2) : 147 - 150

← 1 2 3 4 5 →