沿着某个方向凸的调和单叶映射的构造

本文给出调和单叶映射的凸组合和卷积单叶且沿着某个方向凸的若干充分条件,部分解决Dorf所提出的一个公开问题,相关结果推广和改进早期的一些结论.最后,通过三个例子验证所得到的主要结果.     

Certain geometric properties of the Mittag-Leffler functions

In the present investigation, the Mittag-Leffler functions with their normalization are considered. Several sufficient conditions are obtained so that the Mittag-Leffler functions have certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Partial sums of Mittag-Leffler functions are also studied. The results obtained are new and their usefulness is depicted by deducing several interesting corollaries and examples.     

Absolutely convex,uniformly starlike and uniformly convex harmonic mappings

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi-type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions.     

Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm

In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates.     

A linear operator associated with the Mittag-Leffer function and related conformal mappings

In the present paper, we introduce a linear operator associated with the Mittag-Leffler function. Some convolution properties of meromorphic functions involving this operator are given.     

Geometric properties of basic hypergeometric functions

In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, some useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in a q-close-to-convex family.     

Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators

By making use of a general linear operator , the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses. Some interesting applications involving such and other families of linear operators are also considered. The results presented here include a number of known results as their special cases.     

与条形区域有关的双向单叶解析函数子类的系数估计

本文引入了条形区域内由Salagean算子刻画的解析函数新子类, 讨论了该函数子类的系数估计、Fekete-Szego不等式以及与该函数子类有关的双向单叶函数的系数估计, 所得结果推广了前人的一些工作.     

Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.     

Demiclosed principle and convergence for modified three step iterative process with errors of non-Lipschitzian mappings

A demiclosed principle is proved for asymptotically nonexpansive mappings in the intermediate sense. Moreover, it is proved that the modified three-step iterative sequence converges weakly and strongly to common fixed points of three asymptotically nonexpansive mappings in the intermediate sense under certain conditions. The results of this paper improve and extend the corresponding results of [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling 32 (2000) 1181-1191; G.E. Kim, T.H. Kim, Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces, Comput. Math. Appl. 42 (2001) 1565-1570; B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; K. Nammanee, S. Suantai, The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Appl. Math. Comput. 187 (2007) 669-679; K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320-334] and other corresponding known ones. On the other hand, we show the necessary and sufficient condition for the strong convergence of the modified three-step iterative sequence to some common fixed points of .     

Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators

The object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex meromorphic functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Several interesting integral-preserving properties are also considered.     

Inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the class introduced here.     

On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings

In this paper, several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717] and many others.     

The P1 and P2 approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

The spherical harmonics method in the P₁ and P₂ approximations is used to analyze radiative heat transfer for a space vehicle entering a planet’s atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle’s flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of ?5°.     

Attainment and (sub)differentiability of the infimal convolution of a function and the square of the norm

Let X be a Banach space whose norm is simultaneously LUR and Gateaux (Fréchet) smooth. Under some assumptions, it is shown that the infimal convolution of a fairly general function on X and the square of the norm is generically strongly attained and hence is Gateaux (Fréchet) differentiable. This contains a result of S. Dutta on distance functions.     

DFT calculation for the {2}-inverse of a polynomial matrix with prescribed image and kernel

In this paper, we first give the finite algorithm for generalized inverse of a matrix A over an integral domain, and, based on it and the discrete Fourier transform, present an algorithm for calculating {2}-inverses of a polynomial matrix with prescribed image and kernel. And the algorithm is implemented in the Mathematica programming language and expands the algorithms in [13].