Stability of additive-quadratic ρ-functional equations in Banach spaces: a fixed point approach

被引：4

作者：

Park, Choonkil ^{[1
]}

Kim, Sang Og ^{[2
]}

Alaca, Cihangir ^{[3
]}

机构：

[1] Hanyang Univ, Res Inst Nat Sci, Seoul 04763, South Korea

[2] Hallym Univ, Dept Math, Chunchon 24252, South Korea

[3] Celal Bayar Univ, Dept Math, Muradiye Campus, TR-45140 Manisa, Turkey

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 03期

关键词：

Hyers-Ulam stability; additive-quadratic rho-functional equation; fixed point method; Banach space;

D O I：

10.22436/jnsa.010.03.34

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M(1)f (x, y) : = 3/4 f (x + y) -1/4 f (-x -y) + 1/4 f (x - y) + 1/4 f(y - x) -f (x) -f (y), M(2)f(x, y) : = 2f( x + y/2) + f ( x - y/2 ) + f ( y - x/2 ) -f (x) -f (y). We solve the additive-quadratic rho-functional equations M(1)f (x, y) = rho M(2)f(x, y), (1) and M(2)f(x, y) = rho M(1)f (x, y), (2) where rho is a fixed nonzero number with rho not equal 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive-quadratic rho-functional equations (1) and (2) in Banach spaces. (C)2017 All rights reserved.

引用

页码：1252 / 1262

页数：11

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