共查询到20条相似文献,搜索用时 123 毫秒
1.
Gwang Hui Kim 《数学学报(英文版)》2009,25(1):29-38
The aim of this paper is to study the stability problem of the generalized sine functional equations as follows:
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
2.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
3.
Xin-min Wu Jing-wen Li 《应用数学学报(英文版)》2007,23(3):523-528
In this paper, we deal with a model for the survival of red blood cells with periodic coefficients x'(g)=-μ(t)x(t)+P(t)e^-γ(t)x(t-τ(t)),t≥0.(*)A new sufficient condition for global attractivity of positive periodic solutions of Eq. (*) is obtained. Our criterion improves corresponding result obtained by Li and Wang in 2005. 相似文献
4.
5.
The connection between the functional inequalities
$f\left( {\frac{{x + y}}
{2}} \right) \leqslant \frac{{f\left( x \right) + f\left( y \right)}}
{2} + \alpha _J \left( {x - y} \right), x,y \in D,$f\left( {\frac{{x + y}}
{2}} \right) \leqslant \frac{{f\left( x \right) + f\left( y \right)}}
{2} + \alpha _J \left( {x - y} \right), x,y \in D, 相似文献
6.
Kil-Woung JUN Hark-Mahn KIM 《数学学报(英文版)》2006,22(6):1781-1788
In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f((3x+y)/4)+4f((x+3y)/4)=6f((x+y)/2)+f(x)+f(y),9f((2x+y/3)+9f((x+2y)/3)=16f((x+y)/2+f(x)+f(y)in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta. 相似文献
7.
V. V. Zhuk 《Journal of Mathematical Sciences》2009,157(4):592-606
Let
8.
ZhengQiuZHANG ZhiChengWANG 《数学学报(英文版)》2005,21(1):95-108
We obtain sufficient conditions for the existence of periodic solutions of the following second order nonlinear differential equation:ax(t) bx^2k-1(t) cx^2k-1(t) g(x(t-T1),x(t-T2) ) = p(t) = p(t 2π)Our approach is based on the continuation theorem of the coincidence degree, and the priori estimate of periodic solutions. 相似文献
9.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If E
*(t)=E(t)-2πΔ*(t/2π) with
, then we obtain
10.
O. P. Filatov 《Mathematical Notes》1999,66(3):348-354
For a continuous almost periodic function
, we show that the function
11.
Kenji Nishihara 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):604-614
We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space
12.
Abbas Najati 《数学学报(英文版)》2009,25(9):1529-1542
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation
f(x+y/2+z)-g(x-y/2+z)=h(y). This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 (1978). 相似文献 13.
Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations 总被引:14,自引:0,他引:14
YANGJUN GUANXINPING 《高校应用数学学报(英文版)》1997,12(2):165-178
This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form 相似文献
14.
Abstract
By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Liénard-type equation
15.
Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the form
16.
Jin Deng 《应用数学学报(英文版)》2006,22(1):163-170
In this paper, a nonlinear difference system {xn=βxn-1+f(yn-κ),yn=βyn-1+f(xn-κ),n∈N is considered a,nd sufficient conditions for the existe~lce of the stable 2κ + 1 periodic solution are obtained. 相似文献
17.
S. BERHANU F. CUCCU G. PORRU 《数学学报(英文版)》2007,23(3):479-486
For γ≥1 we consider the solution u=u(x) of the Dirichlet boundary value problem Δu + u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate
u(x)=p(δ(x))[1+A(x)(log 1/δ(x)^-6],
where p(r) ≈ r r√2 log(1/r) near r = 0,δ(x) denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A(x) is a bounded function. For 1 〈 γ 〈 3 we find
u(x)=(γ+1/√2(γ-1)δ(x))^2/γ+[1+A(x)(δ(x))2γ-1/γ+1]
For γ3= we prove that
u(x)=(2δ(x))^1/2[1+A(x)δ(x)log 1/δ(x)] 相似文献
18.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
19.
Xiaomei Wu 《分析论及其应用》2008,24(2):139-148
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi>0,m∑I=1βi=β,0<β<1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献
20.
Linghai ZHANG 《数学年刊B辑(英文版)》2008,29(2):179-198
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0. 相似文献
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