A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

Suppose f is an almost starlike function of orderαon the unit disk D.In this paper,we will prove thatΦ_(n,β_2,γ_2,…,β_n,γ_n)(f)(z)=(f(z_1),((f(z_1)/z_1))~β_2(f′(z_1))~(γ_2)z_2,…, ((f(z_1)/z_1))~(β_n)(f′(z_1))~(γ_n)z_n)′preserves almost starlikeness of orderαonΩ_(n,p_1,p_2,…,p_n)={z= (z_1,z_2,…,z_n)′∈C~n:(sum from j=1 to n)|z_j|~(p_j)<1},where 0相似文献   

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f) on the domain Ωp1,p2,...,pn+1 defined by     

Lowwner链与复Hilbert空间单位球上推广的Roper-Suffridge算子(Ⅰ)

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and order α, almost starlikeness of order α, spirallikeness of type of β and starlikeness.     

The Spirallike Mapping of Type α and the Generalized Roper-Suffridge Operator

In this paper, we get the fact that generalized Roper-Suffridge operators act on spirallike mapping of type α on different domains is invariable, these results include some results known.     

THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER α ON THE UNIT POLYDISK IN Cn

In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sharp estimate of the third homogeneous expan...     

A Note on Weak Type(1,1) Estimate for the Higher Order Commutators of Christ-Journé Type

In this paper,a weak type(1,1)estimate is established for the higher order commutator introduced by Christ and Joume which is defined byT[a1,…,a1]f(x)=p.v∫R^dK(x-y)(lПi=1 mx,yai)·f(y)dy,where K is the standard Calderon-Zygmund convolution kernel on R^d(d≥2)and mx,yai=∫0^1ai(sx+(1-s)y)ds.     

On Growth and Covering Theorem for Strongly Spirallike Mapping of Type β with Order α

In this paper, we deduce growth and covering theorem for f(x) by the other means,where f(x) is strongly spirallike mapping of typeβwith orderαdefined on Unit Ball B of complex Banach space. and still give growth upper bound and distortion upper bound for subordinate mapping.     

A Remark on Pl Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle

In this paper we study the problem of explicit representation and convergence of P′al type(0;1) interpolation and its converse, with some additional conditions,on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of Pn(x) and P′n(x) on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and P′al type interpolations on non-uniformly distributed zeros on the unit circle.     

On the Fekete and Szeg? Problem for Starlike Mappings of Order α

Let S_α~*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class S_α~*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C~n.     

On Growth and Covering Theorem for Spiallike Mapping of Type β with Order α

In this paper,we consider growth and covering theorem for f(x),where f(x)is spiallike mapping of type β with order α defined on unit ball B of complex Banach space,and x=0 is zero of order k+1 for f(x)-x.We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping.This result include some results known.     

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

We use the two mappings satisfying Ⅱ-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings.Also,we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points.The obtained results generalize and improve the corresponding conclusions in references.     

On Growth and Covering Theorem for Almost Spiallike Mapping of Type β with Order α

Let f(x) be an almost spirallike mapping of type β with order α on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f(x), we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.     

A Study on the Second Order Tangent Bundles overBi-K¨ahlerian Manifolds

This paper aims to study the Berger type deformed Sasaki metric gBS on thesecond order tangent bundle T 2M over a bi-K¨ahlerian manifold M. The authors firstly findthe Levi-Civita connection of the Berger type deformed Sasaki metric gBS and calculateall forms of Riemannian curvature tensors of this metric. Also, they study geodesics onthe second order tangent bundle T 2M and bi-unit second order tangent bundle T12,1M,and characterize a geodesic of the bi-unit second order tangent bundle in terms of geodesiccurvatures of its projection to the base. Finally, they present some conditions for a sectionσ : M → T 2M to be harmonic and study the harmonicity of the different canonicalprojections and inclusions of (T 2M, gBS). Moreover, they search the harmonicity of theBerger type deformed Sasaki metric gBS and the Sasaki metric gS with respect to eachother.     

A unified approach to the weighted Grtzsch and Nitsche problems for mappings of finite distortion

This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f with finite linear distortion K(z,f)between two rectangles Q_1 and Q_2 taking vertices into vertices,φ is a positive,increasing and convex function,and λ is a positive weight function.A similar problem of Nitsche-type,which concerns the minimiser of some weighted functional for mappings between two annuli,is also discussed.As by-products,our discussion gives a unified approach to some known results in the literature concerning the weighted Grtzsch and Nitsche problems.     

A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics ℓ1 and ℓ2

Mathematical Notes - A particular class of estimates related to the Nelson–Erd?s–Hadwiger problem is studied. For two types of spaces, Euclidean and spaces with metric ?1,...     

A Necessary and Sufficient Condition for the Solvability of the Nonlinear Schr?dinger Equation on a Finite Interval

The admissibility of the initial-boundary data,which characterizes the existence of solution for the initial-boundary value problem,is important.Based on the Fokas method and the inverse scattering transformation,an approach is developed to solve the initial-boundary value problem of the nonlinear Schrodinger equation on a finite interval.A necessary and sufficient condition for the admissibility of the initial-boundary data is given,and the reconstruction of the potential is obtained.     

A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier–Stokes equations in 2<Emphasis Type=Italic>D</Emphasis>

We show that a velocity field u satisfying the stationary Navier–Stokes equations on the entire plane must be constant under the growth condition lim sup |x|^−α |u(x)| < ∞ as |x| → ∞ for some α ∈ [0, 1/7).^† Bibliography: 10 titles.