A New Variant of Wilson's Functional Equation on Monoids

被引：0

作者：

Dimou, Hajira ^{[1
]}

Elqorachi, Elhoucien ^{[2
]}

Chahbi, Abdellatif ^{[2
]}

机构：

[1] Ibn Zohr Univ, Fac Appl Sci, Lab EEFA, Agadir, Morocco

[2] Ibn Zohr Univ, Fac Sci, Dept Math, Lab EEFA, Agadir, Morocco

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2022年 / 38卷 / 08期

关键词：

Monoid; functional equation; d'Alembert's equation; involutive automorphism; multiplicative function; anti-automorphism;

D O I：

10.1007/s10114-022-1233-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find on a monoid M the complex-valued solutions f, g : M -> C such that f is central and g is continuous of the functional equation f(x sigma(y))+ f(tau(y)x) = 2f (x)g(y), x, y is an element of M, where sigma : M -> M is an involutive automorphism and tau : M -> M is an involutive anti-automorphism. The solutions are described in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of M.

引用

页码：1303 / 1316

页数：14

共 27 条

[1]

Aczel J., 1989, Encycl. Math. Appl., V31

[2] A class of functional equations on a locally compact group [J].

Akkouchi, M ;

Bakali, A ;

Khalil, I .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1998, 57 :694-705

[3] Wilson's functional equation with an anti-endomorphism [J].

Ayoubi, M. ;

Zeglami, D. ;

Aissi, Y. .

AEQUATIONES MATHEMATICAE, 2021, 95 (03) :535-549

[4] A GENERALIZATION OF THE SYMMETRIZED MULTIPLICATIVE CAUCHY EQUATION [J].

Chahbi, A. ;

Fadli, B. ;

Kabbaj, S. .

ACTA MATHEMATICA HUNGARICA, 2016, 149 (01) :170-176

[5] A Variant of d'Alembert Functional Equation on Monoids [J].

Chahbi, Abdellatif ;

Elqorachi, Elhoucien .

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (03) :1127-1142

[6]

D'Alembert J., 1750, HIST ACAD BERLIN, V6, P355

[7]

Davison TMK, 2009, PUBL MATH-DEBRECEN, V75, P41

[8]

Dimou H., 2021, PALESTINE J MATH, V10, P432

[9]

Dimou Hajira, 2019, Proyecciones (Antofagasta), V38, P943, DOI 10.22199/issn.0717-6279-2019-05-0060

[10] Some trigonometric functional equations on monoids generated by their squares [J].

Ebanks, Bruce .

AEQUATIONES MATHEMATICAE, 2021, 95 (02) :383-391

← 1 2 3 →