Existence of continuous solutions for an iterative functional series equation with variable coefficients

被引：4
|
作者：
Murugan, Veerapazham [1 ]
Subrahmanyam, Papagudi Venkatachalam [2 ]
机构：
[1] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Mangalore 575025, India
[2] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India
来源：
AEQUATIONES MATHEMATICAE | 2009年 / 78卷 / 1-2期
关键词：
Iterative functional equations; homeomorphism; Arzela-Ascoli's theorem; Banach's contraction principle; Schauder's fixed point theorem;
D O I：
10.1007/s00010-009-2960-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain theorems on the existence and uniqueness of the solution for iterative functional equations of the type Sigma(infinity)(i=1) lambda(i)(x) H-i (f(i)(x)) = F(x), x is an element of [a, b], where H-i's and F are given functions and lambda(i)'s are nonnegative functions such that Sigma(infinity)(i=1) lambda(i)(x) = 1 on [a, b]. Stability of the solution is also discussed.
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页码：167 / 176
页数：10
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