IJPAM: Volume 117, No. 1 (2017)

Title

NECESSARY AND SUFFICIENT CONDITIONS FOR
SOLUTION OF THE FOURTH ORDER CAUCHY DIFFERENCE
EQUATION ON SYMMETRIC GROUPS

Authors

K. Thangavelu$^1$, M. Pradeep$^2$
$^1$Department of Mathematics
Pachaiyappa's College
Chennai, 600030, Tamilnadu, INDIA
$^2$Department of Mathematics
Arignar Anna Government Arts College
Cheyyar, 604407, Tamilnadu, INDIA

Abstract

Let f: G $\rightarrow$ H be a function, where (G,.) is a group and (H,+) is an abelian group. In this paper, the following Fourth Order Cauchy difference of $f:C^{(4)}f(x_{1},x_{2},x_{3},x_{4},x_{5})\break= f(C_{5}(\prod_{i=1}^{5}x_{i}))... ...i}))+f(C_{1}(\prod_{i=1}^{5}x_{i})) \forall x_{1},x_{2},x_{3},x_{4},x_{5} \in G$ is studied. Where $f(C_{r}(\prod_{i=1}^{n}x_{i}))$ is defined as function of combination $r$ at a time from $n$ objects. Then sufficient and necessary conditions on symmetric groups are obtained.

History

Received: 2017-05-03
Revised: 2017-06-13
Published: November 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 39xx
Key Words and Phrases: Cauchy difference equation, symmetric groups

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How to Cite?

DOI: 10.12732/ijpam.v117i1.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 1
Pages: 45 - 57


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