A note on continuous sums of ridge functions

被引：5

作者：

Aliev, Rashid A. ^{[1
,2
]}

Asgarova, Aysel A. ^{[3
]}

Ismailov, Vugar E. ^{[1
]}

机构：

[1] NAS Azerbaijan, Inst Math & Mech, Baku, Azerbaijan

[2] Baku State Univ, Baku, Azerbaijan

[3] Azerbaijan Univ Languages, Baku, Azerbaijan

来源：

JOURNAL OF APPROXIMATION THEORY | 2019年 / 237卷

关键词：

Cauchy functional equation; Modulus of continuity; Ridge function; APPROXIMATION;

D O I：

10.1016/j.jat.2018.09.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that if a continuous multivariate function is represented by a sum of arbitrarily behaved ridge functions, then, under a suitable condition, it can be represented by a sum of continuous ridge functions. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：210 / 221

页数：12

共 50 条

[1] On the representability of a continuous multivariate function by sums of ridge functions
Aliev, Rashid A.
Isgandarli, Fidan M.
JOURNAL OF APPROXIMATION THEORY, 2024, 304
[2] Continuous sums of ridge functions on a convex body and the class VMO
Kuleshov, A. A.
MATHEMATICAL NOTES, 2017, 102 (5-6) : 799 - 805
[3] Continuous sums of ridge functions on a convex body and the class VMO
A. A. Kuleshov
Mathematical Notes, 2017, 102 : 799 - 805
[4] ON THE REPRESENTATION BY SUMS OF RIDGE FUNCTIONS
Aliev, Rashid A.
Ismailov, Vugar E.
Shahbalayeva, Tarana M.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2015, 41 (02): : 106 - 118
[5] Representation of multivariate functions by sums of ridge functions
Ismailov, Vugar E.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (01) : 184 - 190
[6] On the continuity of finite sums of ridge functions
Konyagin, S. V.
Kuleshov, A. A.
MATHEMATICAL NOTES, 2015, 98 (1-2) : 336 - 338
[7] On the continuity of finite sums of ridge functions
S. V. Konyagin
A. A. Kuleshov
Mathematical Notes, 2015, 98 : 336 - 338
[8] On some properties of smooth sums of ridge functions
A. A. Kuleshov
Proceedings of the Steklov Institute of Mathematics, 2016, 294 : 89 - 94
[9] APPROXIMATION BY SUMS OF RIDGE FUNCTIONS WITH FIXED DIRECTIONS
Ismailov, V. E.
ST PETERSBURG MATHEMATICAL JOURNAL, 2017, 28 (06) : 741 - 772
[10] On Some Properties of Smooth Sums of Ridge Functions
Kuleshov, A. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2016, 294 (01) : 89 - 94

← 1 2 3 4 5 →