共查询到20条相似文献,搜索用时 31 毫秒
1.
P. K. SAHO 《数学学报(英文版)》2005,21(5):1159-1166
In this paper, we determine the general solution of the functional equation f1 (2x + y) + f2(2x - y) = f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 : R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) = g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. 相似文献
2.
G. Zamani Eskandani Pasc Gavruta John M. Rassias Ramazan Zarghami 《Mediterranean Journal of Mathematics》2011,8(3):331-348
In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed
additive and quadratic functional equation
f(lx + y) + f(lx - y) = f(x + y) + f(x - y) + (l- 1)[(l+2)f(x) + lf(-x)],f(\lambda x + y) + f(\lambda x - y) = f(x + y) + f(x - y) + (\lambda - 1)[(\lambda +2)f(x) + \lambda f(-x)], 相似文献
3.
Soon Mo JUNG 《数学学报(英文版)》2006,22(2):583-586
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex) normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ||x|| + ||y|| → ∞ under some suitable conditions. 相似文献
4.
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability
of the functional equation
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