拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (5): 846-859.

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Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces

Wang Chun^1,2, Xu Tianzhou¹

1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081;
2. Department of Mathematics, Changzhi University, Shanxi Changzhi 046011

Received:2016-06-14 Revised:2017-02-27 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11171022)

Abstract

Abstract: This paper establishes the general solution of the mixed type quadratic-additive functional equation
2k[f(x+ky)+f(kx+y)]
=k(1-s+k+ks+2k²)f(x+y)+k(1-s-3k+ks+2k²)f(x-y)
+2kf(kx)+2k(s+k-ks-2k²)f(x)+2(1-k-s)f(ky)+2ksf(y)
with a parameter s, and investigates the Hyers-Ulam-Rassias stability of this functional equation in quasi-Banach spaces, where k > 1 and s ≠1-2k.

Key words: Hyers-Ulam-Rassias stability, General solution, Additive function, Quadratic function, Quasi-Banach space, p-Banach space

CLC Number:

O177.9

Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces[J].Acta mathematica scientia,Series A, 2017, 37(5): 846-859.

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Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces

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