共查询到20条相似文献,搜索用时 15 毫秒
1.
Bing Xu 《Journal of Mathematical Analysis and Applications》2007,329(1):483-497
In this paper we prove the existence and uniqueness of decreasing solutions for the polynomial-like iterative equation so as to answer Problem 2 in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. (China) 24 (1995) 385-405] (or Problem 3 in [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 (2000) 29-36]). Furthermore, we completely investigate increasing convex (or concave) solutions and decreasing convex (or concave) solutions of this equation so that the results obtained in [W. Zhang, K. Nikodem, B. Xu, Convex solutions of polynomial-like iterative equations, J. Math. Anal. Appl. 315 (2006) 29-40] are improved. 相似文献
2.
Aequationes mathematicae - Schauder’s fixed point theorem and the Banach contraction principle are used to study the polynomial-like iterative functional equation $$\begin{aligned} \lambda... 相似文献
3.
Sin-Ei Takahasi Takeshi Miura Hiroyuki Takagi 《Journal of Mathematical Analysis and Applications》2007,329(2):1191-1203
We give the solution of the functional equation f(x+y)+λf(x)f(y)=Φ(x,y) under some conditions. Also we show its Hyers-Ulam stability. 相似文献
4.
Abbas Najati 《Journal of Mathematical Analysis and Applications》2008,340(1):569-574
In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation
f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y). 相似文献
5.
In this paper, by applying the Schauder''s
fixed point theorem we prove the existence of increasing and decreasing solutions of the
polynomial-like iterative equation with variable coefficients
and further completely investigate increasing convex (or concave) solutions and decreasing
convex (or concave) solutions of this equation. The uniqueness and continuous dependence of those solutions
are also discussed 相似文献
6.
Kil-Woung Jun 《Journal of Mathematical Analysis and Applications》2004,299(1):100-112
The purpose of this paper is to solve the stability problem of Ulam for an approximate mapping of the following generalized Pappus' equation:
n2Q(x+my)+mnQ(x−ny)=(m+n)[nQ(x)+mQ(ny)] 相似文献
7.
Dorian Popa 《Journal of Mathematical Analysis and Applications》2011,381(2):530-537
We obtain some results on generalized Hyers-Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions. 相似文献
8.
Dalia Sabina Cîmpean 《Applied mathematics and computation》2010,217(8):4141-4146
We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki-Rassias sense. As a consequence we obtain the Hyers-Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established. 相似文献
9.
10.
In this paper convex solutions and concave solutions of polynomial-like iterative equations are investigated. A result for non-monotonic solutions is given first and applied then to prove the existence of convex continuous solutions and concave ones. Furthermore, another condition for convex solutions, which is weaker in some aspects, is also given. The uniqueness and stability of those solutions are also discussed. 相似文献
11.
Lingxia Liu 《Applied mathematics and computation》2011,217(17):7245-7257
This paper is concern analytic solutions of an iterative functional equation of the form
f(p(z)+q(f(z)))=h(f(z)),z∈C. 相似文献
12.
In this paper, we investigate the general solution and the stability of a cubic functional equation f(x + ny) + f(x - ny) + f(nx) = n^2 f(x + y) + n^2 f(x - y)+ (n^3 - 2n^2 + 2)f(x),where n ≥ 2 is an integer. Furthermore, we prove the stability by the fixed point method. 相似文献
13.
We will find a positive constant Σ2 such that for any 2π ‐periodic function h (t) with zero mean value, the quadratic Newtonian equation x ″ + x2 = σ + h (t) will have exactly two 2π ‐periodic solutions with one being unstable and another being twist (and therefore being Lyapunov stable), provided that the parameter σ is bigger than the first bifurcation value and is smaller than the constant Σ2. The construction of Σ2 is obtained by examining carefully the twist coefficients of periodic solutions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
This paper is concerned with an iterative functional differential equation
c1x(z)+c2x′(z)+c3x″(z)=x(az+bx′(z))