The overdeterminedness of a class of functional equations

Orr Moshe Shalit

doi:10.1007/s00010-007-2889-3

The overdeterminedness of a class of functional equations

Orr Moshe Shalit

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Aczél. It is also shown that functional equations in this class are overdetermined in the sense of Paneah. This means that the solutions, if they exist, are determined by the corresponding relation being fulfilled not in the original domain of validity, but only at the points of a subset of the boundary of the domain of validity.

Original language	English
Pages (from-to)	242-248
Number of pages	7
Journal	Aequationes Mathematicae
Volume	74
Issue number	3
DOIs	https://doi.org/10.1007/s00010-007-2889-3
State	Published - 1 Dec 2007
Externally published	Yes

Keywords

Functional equations on restricted domains
Overdeterminedness

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s00010-007-2889-3

Cite this

@article{56aeeded09fa4897b85beccf5abae6a6,

title = "The overdeterminedness of a class of functional equations",

abstract = "We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Acz{\'e}l. It is also shown that functional equations in this class are overdetermined in the sense of Paneah. This means that the solutions, if they exist, are determined by the corresponding relation being fulfilled not in the original domain of validity, but only at the points of a subset of the boundary of the domain of validity.",

keywords = "Functional equations on restricted domains, Overdeterminedness",

author = "Shalit, {Orr Moshe}",

year = "2007",

month = dec,

day = "1",

doi = "10.1007/s00010-007-2889-3",

language = "English",

volume = "74",

pages = "242--248",

journal = "Aequationes Mathematicae",

issn = "0001-9054",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - The overdeterminedness of a class of functional equations

AU - Shalit, Orr Moshe

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Aczél. It is also shown that functional equations in this class are overdetermined in the sense of Paneah. This means that the solutions, if they exist, are determined by the corresponding relation being fulfilled not in the original domain of validity, but only at the points of a subset of the boundary of the domain of validity.

AB - We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Aczél. It is also shown that functional equations in this class are overdetermined in the sense of Paneah. This means that the solutions, if they exist, are determined by the corresponding relation being fulfilled not in the original domain of validity, but only at the points of a subset of the boundary of the domain of validity.

KW - Functional equations on restricted domains

KW - Overdeterminedness

UR - http://www.scopus.com/inward/record.url?scp=38749103934&partnerID=8YFLogxK

U2 - 10.1007/s00010-007-2889-3

DO - 10.1007/s00010-007-2889-3

M3 - Article

AN - SCOPUS:38749103934

SN - 0001-9054

VL - 74

SP - 242

EP - 248

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 3

ER -

The overdeterminedness of a class of functional equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this