A generalization of d’alembert, jensen and quadratic functional equations on semigroups
Other Title(s)
تصميم المعادلات الدالية دي أليمبرت و جينسن و المعادلة التربيعية على أشباه الزمر
Joint Authors
al-Soosy, Sahar
Asad, Y. Asad
al-Halabi, Samah
Source
IUG Journal of Natural Studies
Issue
Vol. 12, Issue 2 (30 Jun. 2004), pp.69-81, 13 p.
Publisher
The Islamic University-Gaza Deanship of Research and Graduate Affairs
Publication Date
2004-06-30
Country of Publication
Palestine (Gaza Strip)
No. of Pages
13
Main Subjects
Abstract AR
في هذا البحث تم إيجاد الحل العام للمعادلات الدالية التالية 1.
تعميم معادلة دي أليمبرت 2.
تعميمات لمعادلة جينسن 3.
تعميم المعادلة التربيعية، مع العلم أن هذه المعادلات على أشباه زمر.
Abstract EN
In this paper we shall find the general solution g : S1× S2 ×…× Sn→ F of a generalization of d’Alembert equation g (x1 + y1, x2 + y2, …, xn + yn ) +g( x1 y1, x2 + σ2 y2, …, xn + σn yn ) = 2g(x1, x2, …, xn) g(y1, y2,…, yn) ( (x1 , x2,…, xn) (y1, y2 ,…, yn) I S1 × S2 ×…× Sn ) the general solution h : S1× S2 ×…× Sn ×T1× T2 ×…× Tm → G of generalizations of Jensen equation h(x1 + y1, x2 + y2,…, xn + yn, t1, t2,.., tm )+ h(x1 + σ1 y1, x2 + σ2 y2,…, xn + σn yn , t1, t2, .., tm) = 2 h(x1, x2,…, xn, t1, t2,.., tm) (x1, x2,…, xn, t1, t2,..., tm), (y1 ,y2,…,yn, t1, t2,.., tm) I S1× S2 ×…× Sn × T1× T2 ×…× Tm) ) and h( (x1 + y1, t1), ( x2 + y2, t2),…,( xn + yn, tn ) ) + h( (x1 + σ1y1, t1), ( x2 + σ2y2 , t2,) xn + σnyn, tn ) ) = 2 h( (x1 , t1), ( x2 , t2), …, xn, tn ) (x1 , x2,…, xn), (y1 y2,…, yn,), (t1 ,t2,…, tn) I S1× S2 ×…× Sn, and the general solution k : S1 × S2 ×…× Sn→ F of a generalization of the quadratic equation k( x1 + y1, x2 + y2 , …, xn + yn ) + k( x1 + σ1 y1, x2 + σ2 y2, …, xn + n yn ) 2= k(x1, x2, …, xn)+ 2k(y1, y2,…, yn) ( (x1, x2,…, xn), (y1, y2, …, yn) I S1× S2 ×…× Sn), where S1,S2,…,Sn,T1, T2,…, and Tm are commutative semi groups ,F is a quadratic ally closed field of characteristic different from 2, G is a 2-cancelative Aeolian group, H is an Aeolian group uniquely divisible by 2 and for each i = 1, 2,…n, σi is an endomorphism of Si with σi (σi xi) = xi.
American Psychological Association (APA)
Asad, Y. Asad& al-Halabi, Samah& al-Soosy, Sahar. 2004. A generalization of d’alembert, jensen and quadratic functional equations on semigroups. IUG Journal of Natural Studies،Vol. 12, no. 2, pp.69-81.
https://search.emarefa.net/detail/BIM-159680
Modern Language Association (MLA)
Asad, Y. Asad…[et al.]. A generalization of d’alembert, jensen and quadratic functional equations on semigroups. IUG Journal of Natural Studies Vol. 12, no. 2 (Jun. 2004), pp.69-81.
https://search.emarefa.net/detail/BIM-159680
American Medical Association (AMA)
Asad, Y. Asad& al-Halabi, Samah& al-Soosy, Sahar. A generalization of d’alembert, jensen and quadratic functional equations on semigroups. IUG Journal of Natural Studies. 2004. Vol. 12, no. 2, pp.69-81.
https://search.emarefa.net/detail/BIM-159680
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 81
Record ID
BIM-159680