共查询到20条相似文献,搜索用时 31 毫秒
1.
Ting-Bin Cao 《Journal of Mathematical Analysis and Applications》2009,352(2):739-281
We consider the complex differential equations of the form
Ak(z)f(k)+Ak−1(z)f(k−1)+?+A1(z)f′+A0(z)f=F(z), 相似文献
2.
In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k+12. If fn + af(k) and gn + ag(k) share b CM and the b-points of fn + af(k) are not the zeros of f and g, then f and g are either equal or closely related. 相似文献
3.
Let F be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ F, all of whose zeros have multiplicity at least k + 1, and f + a(f^(k))^n≠b in D, then F is normal in D. 相似文献
4.
E. Jiménez Fernández 《Journal of Mathematical Analysis and Applications》2011,383(1):130-136
Consider a Banach function space X(μ) of (classes of) locally integrable functions over a σ-finite measure space (Ω,Σ,μ) with the weak σ-Fatou property. Day and Lennard (2010) [9] proved that the theorem of Komlós on convergence of Cesàro sums in L1[0,1] holds also in these spaces; i.e. for every bounded sequence n(fn) in X(μ), there exists a subsequence k(fnk) and a function f∈X(μ) such that for any further subsequence j(hj) of k(fnk), the series converges μ-a.e. to f. In this paper we generalize this result to a more general class of Banach spaces of classes of measurable functions — spaces L1(ν) of integrable functions with respect to a vector measure ν on a δ-ring — and explore to which point the Fatou property and the Komlós property are equivalent. In particular we prove that this always holds for ideals of spaces L1(ν) with the weak σ-Fatou property, and provide an example of a Banach lattice of measurable functions that is Fatou but do not satisfy the Komlós Theorem. 相似文献
5.
Our main result is as follows: let f and a be two entire functions such that \(\max \{ \rho _2 (f),\rho _2 (a)\} < \tfrac{1} {2}\) . If f and f (k) a CM, and if ρ(a (k) ? a) < ρ(f ? a), then f (k) ? a = c(f ? a) for some nonzero constant c. This result is applied to improve a result of Gundersen and Yang. 相似文献
6.
Zhongqiu Ye 《Journal of Mathematical Analysis and Applications》2003,283(2):689-695
Let f∈S, f be a close-to-convex function, fk(z)=[f(zk)]1/k. The relative growth of successive coefficients of fk(z) is investigated. The sharp estimate of ||cn+1|−|cn|| is obtained by using the method of the subordination function. 相似文献
7.
S. R. Nasyrov 《Mathematical Notes》2007,82(5-6):798-802
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. 相似文献
8.
Let f be a nonconstant entire function, and let k (?2) be an integer. We denote by the set consisting of all the fixed points of f. This paper proves that if f and f′ have the same fixed points, namely, Ef(z)=Ef′(z), and if f(k)(z)=z whenever f(z)=z, then f≡f′. 相似文献
9.
Joseph Blum 《Journal of Combinatorial Theory, Series A》1974,17(2):156-161
Let f(n) denote the number of square permutations in the symmetric group Sn. This paper proves a conjecture that f(2k + 1) = (2k + 1)f(2k) and provides efficient procedures for the computation of f(n). The behavior of f(n) as n → ∞ is investigated and an asymptotic result obtained which shows that f(n) ~ 2Knne?n, where . 相似文献
10.
M. Eshaghi Gordji H. Khodaei 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5629-5643
In this paper, we achieve the general solution and the generalized Hyers–Ulam–Rassias stability of the following functional equation
f(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)