Existence and uniqueness of solutions of Hahn difference equations

被引：40
|
作者：
Hamza, Alaa E. [1 ]
Ahmed, Samah M. [2 ]
机构：
[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt
[2] Al Azhar Univ, Fac Sci, Dept Math, Girls Branch, Cairo, Egypt
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2013年
关键词：
Hahn difference operator; Jackson q-difference operator;
D O I：
10.1186/1687-1847-2013-316
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Hahn introduced the difference operator D(q,omega)f(t) = (f(qt + omega) - f(t))/(t(q - 1) + omega) in 1949, where 0 < q < 1 and omega > 0 are fixed real numbers. This operator extends the classical difference operator Delta(omega)f(t) = (f(t + omega) - f (t))/omega as the Jackson q-difference operator D(q)f(t) = (f(qt) - f(t))/(t(q - 1)). In this paper, we present new results of the calculus based on the Hahn difference operator. Also, we establish an existence and uniqueness result of solutions of Hahn difference equations by using the method of successive approximations.
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页数：15
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