ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION

被引：1

作者：

Lee, Jung Rye ^{[1
,2
]}

Lee, Sung Jin ^{[1
,2
]}

Park, Choonkil

机构：

[1] Daejin Univ, Dept Math, Kyeonggi 487711, South Korea

[2] Hanyang Univ, Dept Math, Res Inst Nat Sci, Seoul 133791, South Korea

来源：

KOREAN JOURNAL OF MATHEMATICS | 2013年 / 21卷 / 01期

关键词：

Ulam-Hyers stability; orthogonally additive and orthogonally quadratic functional equation; fi xed point; non-Archimedean normed space; orthogonality space;

D O I：

10.11568/kjm.2013.21.1.1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation f(x/2 + y) + f(x/2 - y) + f(x/2 + z) + f(x/2 - z) (0.1) = 3/2f(x) - 1/2f(-x) + f(y) + f(-y) + f(z) + f(-z) for all x, y, z with x perpendicular to y, in orthogonality Banach spaces and in non- Archimedean orthogonality Banach spaces.

引用

页码：1 / 21

页数：21

共 50 条

[11] On orthogonally additive band operators and orthogonally additive disjointness preserving operators
Turan, Bahri
Tulu, Demet
TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (04) : 1258 - 1266
[12] ORTHOGONALLY ADDITIVE AND ORTHOGONALLY MULTIPLICATIVE HOLOMORPHIC FUNCTIONS OF MATRICES
Bu, Qingying
Liao, Chingjou
Wong, Ngai-Ching
ANNALS OF FUNCTIONAL ANALYSIS, 2014, 5 (02) : 80 - 89
[13] Orthogonally additive bijections are additive
Karol Baron
Aequationes mathematicae, 2015, 89 : 297 - 299
[14] Orthogonally additive bijections are additive
Baron, Karol
AEQUATIONES MATHEMATICAE, 2015, 89 (02) : 297 - 299
[15] ON ORTHOGONALLY ADDITIVE FUNCTIONALS
DREWNOWSKI, L
ORLICZ, W
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1968, 16 (11): : 883 - +
[16] STABILITY OF A QUARTIC AND ORTHOGONALLY QUARTIC FUNCTIONAL EQUATION
Arunkumar, M.
Ravi, K.
Rassias, M. J.
BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 3 (03): : 13 - 24
[17] On orthogonally additive functions
Baron, K
Volkmann, P
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1998, 52 (3-4): : 291 - 297
[18] On a ρ-Orthogonally Additive Mappings
Chmielinski, Jacek
Sikorska, Justyna
Wojcik, Pawel
RESULTS IN MATHEMATICS, 2020, 75 (03)
[19] ORTHOGONALLY ADDITIVE AND ORTHOGONALLY INCREASING FUNCTIONS ON VECTOR-SPACES
GUDDER, S
STRAWTHER, D
PACIFIC JOURNAL OF MATHEMATICS, 1975, 58 (02) : 427 - 436
[20] Narrow orthogonally additive operators
Pliev, Marat
Popov, Mikhail
POSITIVITY, 2014, 18 (04) : 641 - 667

← 1 2 3 4 5 →