摘要：
In this paper, by using the contraction mapping principle and
constructing a suitable Lyapunov functional, we established a set of easily
applicable criteria for the existence, uniqueness and global attractivity of
positive periodic solution and positive almost periodic solution of a neutral
multi-species Logarithmic population model with multiple delays and impulses.
The results improve and generalize the known ones in [1], as an
application, we also give an example to illustrate the feasibility of our main
results.
摘要：
In this paper, we investigate the properties of mappings in harmonic Bergman spaces. First, we discuss the coefficient estimate, the Schwarz-Pick Lemma and the Landau-Bloch theorem for mappings in harmonic Bergman spaces in the unit disk
$$\mathbb D $$
of
$$\mathbb C $$
. Our results are generalizations of the corresponding ones in Chen et al. (Proc Am Math Soc 128:3231–3240, 2000), Chen et al. (J Math Anal Appl 373:102–110, 2011), Chen et al. (Ann Acad Sci Fenn Math 36:567–576, 2011). Then, we study the Schwarz-Pick Lemma and the Landau-Bloch theorem for mappings in harmonic Bergman spaces in the unit ball
$$\mathbb B ^{n}$$
of
$$\mathbb C ^{n}$$
. The obtained results are generalizations of the corresponding ones in Chen and Gauthier (Proc Am Math Soc 139:583–595 2011). At last, we get a characterization for mappings in harmonic Bergman spaces on
$$\mathbb B ^{n}$$
in terms of their complex gradients.
作者：
Zhenghui Gao;Liu Yang;Gang Liu;Hengyang Normal University;Hengyang;...
期刊：
应用数学(英文),2013年4(6):859-863 ISSN：2152-7385
作者机构：
Department of Mathematics and Computational Science
关键词：
Caputo;FRACTIONAL;Derivative;IMPULSES;NONLOCAL;Conditions;EXISTENCE;UNIQUENESS;Fixed;Point;Impulses;Nonlocal Conditions;Existence;Uniqueness;Fixed Point
摘要：
In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.
期刊：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2013年88(1):143-157 ISSN：0004-9727
通讯作者：
Chen, Sh
作者机构：
[Chen, Sh] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, S.] Indian Stat Inst, Chennai Ctr, SETS, MGR Knowledge City, Chennai 600113, Tamil Nadu, India.;[Vuorinen, M.] Univ Turku, Dept Math, Turku 20014, Finland.;[Wang, X.] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China.
通讯机构：
[Chen, Sh] H;Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India.;[Ponnusamy, Saminathan] SETS, Chennai Ctr, Indian Stat Inst, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] S;SETS, Chennai Ctr, Indian Stat Inst, CIT Campus, Madras 600113, Tamil Nadu, India.
关键词：
Close-to-convex;Convex;Partial sum;Starlike and univalent harmonic mappings
摘要：
If S denotes the class of functions h(z) = z + Sigma(infinity)(n=2) a(n)Z(n) which are analytic and univalent in the unit disk vertical bar z vertical bar < 1, then the classical result of Szego shows that every section s(n)(h)(z) = Sigma(n)(k=1) a(k)z(k) of h is univalent in vertical bar z vertical bar < 1/4. Exact (largest) radius of univalence r(n) of s(n)(h) remains an open problem, although the corresponding results for sections of various geometric subclasses of S have been obtained which include those h is an element of S for which Re h'(z) > 0 holds in the unit disk. However, no attempt has been made to derive harmonic analog of these results. The central object in this case is the class S-H(0) of sense-preserving harmonic univalent mappings f = h+(g) over bar defined on the unit disk, normalized so that h(0) = g(0) = h'(0) - 1 = g'(0) = 0. Our primary objective in this paper is to solve the univalency of every section of a harmonic function in the class P-H(0)(alpha), where P-H(0)(alpha) denotes the class of normalized univalent harmonic mapping f = h+(g) over bar in the unit disk vertical bar z vertical bar < 1 satisfying the condition Re(h'(z) - alpha) > vertical bar g'(z)vertical bar for vertical bar z vertical bar < 1, where g'(0) = 0 and 0 <= alpha < 1. In this paper, we first present sharp bounds for the moduli of the coefficients a(n), b(n) of f is an element of P-H(0)(alpha) and then determine the value of r so that the partial sums of f is an element of P-H(0) are close-to-convex in vertical bar z vertical bar < r. (C) 2013 Elsevier Ltd. All rights reserved.
