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

[41] 2-FARTHEST ORTHOGONALITY IN GENERALIZED 2-NORMED SPACES
Abad, S. M. Mousav Shams
Mazaheri, H.
Dehghan, M. A.
JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY, 2018, 24 (01) : 71 - 78
[42] ON SYMMETRY OF BIRKHOFF-JAMES ORTHOGONALITY OF LINEAR OPERATORS ON FINITE-DIMENSIONAL REAL BANACH SPACES
Sain, Debmalya
Ghosh, Puja
Paul, Kallol
OPERATORS AND MATRICES, 2017, 11 (04): : 1087 - 1095
[43] INNER AND OUTER J-RADII OF CONVEX-BODIES IN FINITE-DIMENSIONAL NORMED SPACES
GRITZMANN, P
KLEE, V
DISCRETE & COMPUTATIONAL GEOMETRY, 1992, 7 (03) : 255 - 280
[44] On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces
Javier Alonso
Horst Martini
Senlin Wu
Aequationes mathematicae, 2012, 83 : 153 - 189
[45] On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces
Alonso, Javier
Martini, Horst
Wu, Senlin
AEQUATIONES MATHEMATICAE, 2012, 83 (1-2) : 153 - 189
[46] EMBEDDINGS OF FINITE-DIMENSIONAL SPACES INTO FINITE PRODUCTS OF 1-DIMENSIONAL SPACES
OLSZEWSKI, W
TOPOLOGY AND ITS APPLICATIONS, 1991, 40 (01) : 93 - 99
[47] FINITE-DIMENSIONAL LOCALLY BOUNDED SPACES
IYAHEN, SO
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 6 (MAY): : 488 - 490
[48] Finite-Dimensional Bicomplex Hilbert Spaces
Lavoie, Raphael Gervais
Marchildon, Louis
Rochon, Dominic
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2011, 21 (03) : 561 - 581
[49] On maps that preserve orthogonality in normed spaces
Blanco, A.
Turnsek, A.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 : 709 - 716
[50] OPERATORS REVERSING ORTHOGONALITY IN NORMED SPACES
Chmielinski, Jacek
ADVANCES IN OPERATOR THEORY, 2016, 1 (01): : 8 - 14

← 1 2 3 4 5 →