On restricted functional inequalities associated with quadratic functional equations

被引：4

作者：

Tareeghee, M. A. ^{[1
]}

Najati, A. ^{[1
]}

Abdollahpour, M. R. ^{[1
]}

Noori, B. ^{[1
]}

机构：

[1] Univ Mohaghegh Ardabili, Fac Sci, Dept Math, Ardebil, Iran

来源：

AEQUATIONES MATHEMATICAE | 2022年 / 96卷 / 04期

关键词：

Hyers-Ulam stability; Quadratic functional equation; Quadratic mapping; Approximate quadratic mapping; Asymptotic behavior; ULAM-RASSIAS STABILITY;

D O I：

10.1007/s00010-022-00872-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper it is proved that, for a function f : chi -> E mapping from a normed linear space chi into an inner product space E, the functional inequality parallel to 2 f(x) + 2f(y) - f (x - y) parallel to <= parallel to f (x + y)parallel to, parallel to x parallel to + parallel to y parallel to >= d for some d > 0, implies f is quadratic. Other types of functional inequalities related to the quadratic functional equation have also been investigated. Besides we establish the Hyers-Ulam stability on restricted domains, and we improve the bounds and thus the stability results obtained in Jung (J Math Anal Appl 222:126-137, 1998) and Rassias (J Math Anal Appl 276: 747-762, 2002). Finally we apply our recent results to the asymptotic behavior of quadratic functional equations of different types.

引用

页码：763 / 772

页数：10

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