共查询到20条相似文献,搜索用时 31 毫秒
1.
Aequationes mathematicae - Our main result is that we describe the solutions $$g,f:S\rightarrow \mathbb {C}$$ of the functional equation $$\begin{aligned} g(x\sigma (y))=g(x)g(y)-f(x)f(y)+\alpha... 相似文献
2.
Aequationes mathematicae - Let S be a semigroup. We describe the solutions $$f,g:S \rightarrow \mathbb {C}$$ of the functional equation $$\begin{aligned} f(xy) = f(x)g(y) + g(x)f(y) - g(x)g(y), \... 相似文献
3.
Aequationes mathematicae - Let G be a group, and let $$\chi $$ and $$\mu $$ be characters of G. We find the solutions of the functional equation $$f(xy) = f(x)\chi (y) + \mu (x)f(y)$$ , $$x,y \in... 相似文献
4.
Piotr Migus 《Archiv der Mathematik》2019,112(4):395-405
Let
$$f,g:({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^m,0)$$
be
$$C^{r+1}$$
mappings and let
$$Z=\{x\in \mathbf {\mathbb {R}}^n:\nu (df (x))=0\}$$
,
$$0\in Z$$
,
$$m\le n$$
. We will show that if there exist a neighbourhood U of
$$0\in {\mathbb {R}}^n$$
and constants
$$C,C'>0$$
and
$$k>1$$
such that for
$$x\in U$$
$$\begin{aligned}&\nu (df(x))\ge C{\text {dist}}(x,Z)^{k-1}, \\&\left| \partial ^{s} (f_i-g_i)(x) \right| \le C'\nu (df(x))^{r+k-|s|}, \end{aligned}$$
for any
$$i\in \{1,\dots , m\}$$
and for any
$$s \in \mathbf {\mathbb {N}}^n_0$$
such that
$$|s|\le r$$
, then there exists a
$$C^r$$
diffeomorphism
$$\varphi :({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^n,0)$$
such that
$$f=g\circ \varphi $$
in a neighbourhood of
$$0\in {\mathbb {R}}^n$$
. By
$$\nu (df)$$
we denote the Rabier function. 相似文献
5.
Aequationes mathematicae - In this paper, we determine the central solutions $$f:G\times G\rightarrow {{\mathbb {C}}}$$ of the functional equation $$\begin{aligned} f(x_1\sigma y_1,x_2\tau... 相似文献
6.
该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件. 相似文献
7.
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
8.
Abdellatif Ghendir Aoun 《应用数学年刊》2017,33(4):340-352
In this paper, we study a fractional differential equation $$^{c}D^{\alpha}_{0^{+}}u(t)+f(t,u(t))=0,\quad t\in(0, +\infty)$$ satisfying the boundary conditions:
$$u^{\prime}(0)=0,\quad \lim_{t\rightarrow +\infty}\,^{c}D^{\alpha-1}_{0^{+}}u(t)=g(u),$$ where $1<\alpha\leqslant2$, $^{c}D^{\alpha}_{0^{+}}$ is the standard Caputo fractional derivative of order $\alpha$. The main tools used in the paper is contraction principle in the Banach space and the fixed point theorem due to
D. O''Regan. Some the compactness criterion and existence of solutions are established. 相似文献
9.
10.
Periodica Mathematica Hungarica - We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all $$x\in [0,1]$$ , $$\beta \ge {\beta... 相似文献
11.
Hoang Xuan Phu 《Mathematical Methods of Operations Research》2008,67(2):207-222
A real-valued function f defined on a convex subset D of some normed linear space is said to be inner γ-convex w.r.t. some fixed roughness degree γ > 0 if there is a such that holds for all satisfying ||x
0 − x
1|| = νγ and . This kind of roughly generalized convex functions is introduced in order to get some properties similar to those of convex
functions relative to their supremum. In this paper, numerous properties of their supremizers are given, i.e., of such satisfying lim . For instance, if an upper bounded and inner γ-convex function, which is defined on a convex and bounded subset D of some inner product space, has supremizers, then there exists a supremizer lying on the boundary of D relative to aff D or at a γ-extreme point of D, and if D is open relative to aff D or if dim D ≤ 2 then there is certainly a supremizer at a γ-extreme point of D. Another example is: if D is an affine set and is inner γ-convex and bounded above, then for all , and if 2 ≤ dim D < ∞ then each is a supremizer of f.
相似文献
12.
奇异非线性$p-$调和方程的一类正整体解 总被引:2,自引:0,他引:2
设p>1,β≥0是常数, n是自然数, 是一个连续函数.本文研究形如的奇异非线性p-调和方程的正整体解,给出了该类方程具有无穷多个其渐近阶刚好为|x|(2n-2)(当|x|→∞时)的径向对称的正整体解的若干充分条件. 相似文献
13.
Dvid Kunszenti-Kovcs 《Archiv der Mathematik》2019,112(2):205-212
Extending a result by Chilin and Litvinov, we show by construction that given any
$$\sigma $$
-finite infinite measure space
$$(\Omega ,\mathcal {A}, \mu )$$
and a function
$$f\in L^1(\Omega )+L^\infty (\Omega )$$
with
$$\mu (\{|f|>\varepsilon \})=\infty $$
for some
$$\varepsilon >0$$
, there exists a Dunford–Schwartz operator T over
$$(\Omega ,\mathcal {A}, \mu )$$
such that
$$\frac{1}{N}\sum _{n=1}^N (T^nf)(x)$$
fails to converge for almost every
$$x\in \Omega $$
. In addition, for each operator we construct, the set of functions for which pointwise convergence fails almost everywhere is residual in
$$L^1(\Omega )+L^\infty (\Omega )$$
. 相似文献
14.
Acta Mathematica Hungarica - The sine addition formula on a semigroup S is the functional equation $$f(xy) = f(x)g(y) + g(x)f(y)$$ for all $$x,y \in S$$ . For some time the solutions have been... 相似文献
15.
Aequationes mathematicae - The aim of this work is to investigate the alternative quadratic functional equation $$\begin{aligned} f(x+y)+f(x-y)-2f(x)-2f(y)\in \{0,1,2\}, \end{aligned}$$ where $$f{:... 相似文献
16.
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
17.
本文研究一类二阶脉冲微分方程:■的正解存在性.其中,0<η<1,0<α<1,f:[0,1]×[0,∞)×R→[0,∞),I_i:[0,∞)×R→R,J_i:[0,∞)×R→R,(i=1,2,…,k)均为连续函数.本文所用方法是文献[5]推广的Krasnoselskii不动点定理,此定理为解决依赖于一阶导数的边值问题提供了理论依据.基于此定理,获得了问题正解存在性定理.特别地,我们获得此类问题的Green函数,使问题的解决更直观和简单. 相似文献
18.
A new hyperstability result for the Apollonius equation on a restricted domain and some applications
Let \((G,+)\) be an abelian group equipped with a complete ultrametric d that is invariant (i.e., \(d(x + z, y + z)= d(x, y\)) for \(x, y, z \in G\)), X be a normed space and \(U\subset X\setminus \{0\} \) be a nonempty subset. Under some weak natural assumptions on U and on the function \(\chi :U^3\rightarrow [0,\infty )\), we study new hyperstability results when \(f:U\rightarrow G\) satisfy the following Apollonius inequality Moreover, we derive some consequences from our main results.
相似文献
$$\begin{aligned}&d\Big (4f\Big (z-\frac{x+y}{2}\Big )+f(x-y),2f(x-z)+2f(y-z)\Big )\leqslant \chi (x,y,z),\\ {}&\quad x, y, z\in U,\;\;x-z,y-z,x-y,z-\frac{x+y}{2}\in U. \end{aligned}$$
19.
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
20.
Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities 下载免费PDF全文
In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
相似文献