摘要
该文讨论了带有参数s的二次-可加混合型函数方程2k[f(x+ky)+f(kx+y)]=k(1-s+k+ks+2k~2)f(x+y)+k(1-s-3k+ks+2k~2)f(x-y)+2kf(kx)+2k(s+k-ks-2k~2)f(x)+2(1-k-s)f(ky)+2ksf(y)的一般解,同时研究了该函数方程在拟Banach空间上的Hyers-Ulam-Rassias稳定性,这里k>1,s≠1-2k.
This paper establishes the general solution of the mixed type quadratic-additive functional equation2 k[f(x+ky)+f(kx+y)]=k(1-s+k+ks+2 k~2)f(x+y)+k(1-s-3 k+ks+2 k~2)f(x-y)+2 kf(kx)+2 k(s+k-ks-2 k~2)f(x)+2(1-k-s)f(ky)+2 ksf(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≠1-2 k.
引文
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