共查询到20条相似文献,搜索用时 109 毫秒
1.
Kil-Woung Jun 《Journal of Mathematical Analysis and Applications》2004,297(1):70-86
In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ? is defined by f(x∗y)+f(x∗y−1)−2g(x)−2g(y)=?(x,y), f(x∗y)+g(x∗y−1)−2h(x)−2k(y)=?(x,y), where (G,∗) is a group, X is a real or complex Hausdorff topological vector space and f,g,h,k are functions from G into X. 相似文献
2.
Let G be an Abelian group with a metric d and E a normed space. For any f:G→E we define the quadratic difference of the function f by the formula
Qf(x,y):=2f(x)+2f(y)−f(x+y)−f(x−y) 相似文献
3.
Vladimir Drobot 《Aequationes Mathematicae》1970,5(1):120-122
It is well known ([1], [3]) that any measurable solution of the Cauchy functional equationf(x+y)=f(x)+f(y) must actually be continuous. The same is true of some other functional equations likef(x+y)=f(x)f(y),f(x+y)f(x–y)=f(x)
2
–f(y)
2, etc. (cf. [1]). In this note we prove a general result of this type for functional equations on groups. 相似文献
4.
Xiaojing Yang 《Journal of Mathematical Analysis and Applications》2004,296(2):708-718
In this paper, the unbounded solutions for the following nonlinear planar system:
x′=a+y+−a−y−+f(t),y′=−b+x++b−x−+g(t), 相似文献
5.
该文研究了2-Banach空间上三次-四次混合型函数方程f(kx+y)+f(kx-y)=(k^2+k)/2[f(x+y)+f(x-y)]+(k^2-k)/2[f(-x-y)+f(y-x)]+(k^4+k^3-k^2-k)f(x)+(k^4-k^3-k^2+k)f(-x)-(k^2-1)f(y)-(k^2-1)f(-y)的一般解和Hyers-Ulam-Rassias稳定性,这里k>1.该文的结果提升和推广了已有的相关结果. 相似文献
6.
Włodzimierz Fechner 《Aequationes Mathematicae》2014,87(1-2):71-87
The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) $$f(x+y)+f(y+z)+f(x+z)\leq f(x+y+z)+f(x)+f(y)+f(z)$$ for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: $$\|x+y\|+\|y+z\|+\|x+z\|\leq\|x+y+z\|+\|x\|+\|y\|+\|z\|,$$ which in particular holds true for all x, y, z from a real or complex inner product space. 相似文献
7.
Let $$(G,+)$$ be a commutative semigroup, $$\tau $$ be an endomorphism of G and involution, D be a nonempty subset of G, and $$(H,+)$$ be an abelian group, uniquely divisible by 2. Motivated by the extension problem of J. Aczél and the stability problem of S.M. Ulam, we show that if the set D is “sufficiently large”, then each function $$g{:} D\rightarrow H$$ such that $$g(x+y)+g(x+\tau (y))=2g(x)+2g(y)$$ for $$x,y\in D$$ with $$x+y,x+\tau (y)\in D$$ can be extended to a unique solution $$f{:} G\rightarrow H$$ of the functional equation $$f(x+y)+f(x+\tau (y))=2f(x)+2f(y)$$. 相似文献
8.
白定勇 《数学物理学报(A辑)》2003,23(1):38-44
考虑二阶微分系统边值问题[JB({]x″(t)+λ f(t,x(t),y(t))=0,\=y″(t)+μ g(t,x(t),y(t))=0,\ 00, f, g:[0,1]×[0,∞)×[0,∞)→R连续. 突破了以往文献要求非线性项 f, g非负的限制,运用锥上的一个不动点定理,在半正的情形下建立了问题正解的存在性 相似文献
9.
在赋范线性空间中考察下列几类泛函方程( ) f(x) g(y) =h(x+y) , ( ) f(x+y) =f(x) f(y) , ( ) f(x+y) =f(x) +f(y) +ag(x) g(y)的性质与解以及彼此之间的关系 . 相似文献
10.
对于凸函数建立了几个新的 Hadamard型不等式 ,比如f ∑nk=1qkak∫A+yA- yg(x) dx ∫A+yA- yf (x) g(x) dx ∑nk=1qkf (ak) ∫A+yA- yg(x) dx和f (pa +qb) p∫ξaf (x) g(x) dx∫ξag(x) dx+q∫bξf (x) g(x) dx∫bξg(x) dx pf (a) +qf (b)等 ,推广了前人所做的工作 . 相似文献
11.
本文运用 Liapunov第二方法 ,研究了食饵有常数放养率的广义 Rosenzweig-Macarthur系统x=f ( x) -yφ( x) +H ,y=h( y) [-e+Kφ( x) ]唯一正平衡点的稳定性 .并利用 Poincare-Bendixon环域定理及张芷芬唯一性定理 ,论证了在 R+ 2 ={( x,y)∶x>0 ,y>0 }内极限环的存在唯一性及其稳定性 . 相似文献
12.
Ziying Lu Gang Lu Yuanfeng Jin Choonkil Park 《Journal of Applied Analysis & Computation》2019,9(6):2295-2307
In this paper, we investigate the following $(\alpha,\beta)$-functional equations
$$
2f(x)+2f(z)=f(x-y)+\alpha^{-1}f(\alpha
(x+z))+\beta^{-1}f(\beta(y+z)),~~~~~~~~~(0.1)
$$
$$
2f(x)+2f(y)=f(x+y)+\alpha^{-1}f(\alpha(x+z))
+\beta^{-1}f(\beta(y-z)),~~~~~~~~~~~(0.2)
$$
where $\alpha,\beta$ are fixed nonzero real numbers with $\alpha^{-1}+\beta^{-1}\neq 3$.
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the $(\alpha,\beta)$-functional equations $(0.1)$ and $(0.2)$ in non-Archimedean Banach spaces. 相似文献
13.
Using the direct method,we investigate the generalized Hyers-Ulam stability of the following quadratic functional inequality■inβ-homogeneous complex Banach spaces. 相似文献
14.
In this paper, the equivalence of the two functional equations $$f\left(\frac{x+y}{2} \right)+f\left(\sqrt{xy} \right)=f(x)+f(y)$$ and $$2f\left(\mathcal{G}(x,y)\right)=f(x)+f(y)$$ will be proved by showing that the solutions of either of these equations are constant functions. Here I is a nonvoid open interval of the positive real half-line and ${\mathcal{G}}$ is the Gauss composition of the arithmetic and geometric means. 相似文献
15.
Tingxiu Wang 《Journal of Mathematical Analysis and Applications》2004,298(1):33-44
There have been a lot of investigations about stability of the linear scalar functional differential equation
x′(t)=a(t)x(t)+b(t)x(t−h), 相似文献
16.
Aequationes mathematicae - The aim of this work is to investigate the alternative quadratic functional equation $$\begin{aligned} f(x+y)+f(x-y)-2f(x)-2f(y)\in \{0,1,2\}, \end{aligned}$$ where $$f{:... 相似文献
17.
Modular functions on a lattice (m(x)+m(y)=m(x∪y)+m(x∩y)) live on modular lattices in that they are induced by modular functions on a quotient modular lattice. Those which identify
pairs of the distributive inequality live on distributive lattices in the same sense. The structure of all modular functions
on a lattice of finite height is determined. The “distance function” derived by Kranz from a modular function is shown to
satisfy the triangle inequality.
Presented by E. Nelson. 相似文献
18.
Results in Mathematics - We observe that the Hermite–Hadamard inequality written in the form $$f\left(\frac{x+y}{2}\right)\leq\frac{F(y)-F(x)}{y-x}\leq\frac{f(x)+f(y)}{2}$$ may be viewed as... 相似文献
19.
Monatshefte für Mathematik - An extension of the linearity of the continuous solutions of the functional equation $$f(x+y)=f(x)+f(y)$$ to measurable functions is presented. 相似文献
20.
In this paper, the authors investigate the general solution of a new cubic functional equation \(\begin{equation*} 3f(x+3y)-f(3x+y)=12[f(x+y)+f(x-y)]+80f(y)-48f(x) \end{equation*}\) and discuss its generalized Hyers - Ulam - Rassias stability in Banach spaces and stability in fuzzy normed spaces. 相似文献