The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions■are given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions■are sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classic...     

Some Theorems of Analytic Functions

1 Introduction We denote that: σ—the class of functions ω(z)=A_1z+A_2z~2+…regular in the unit disk such that sum from n=1 to ∞ (n|A_n|~2<∞);K_c— the class of close-to-convex function f(z),that is, if f(z)=α_1z+α_2z~2+…there exists a starlike function g(z) =b_1z+b_2z~2+…such that     

A Spirallikeness Condition for Analytic Functions

Letα,β,γandρbe real,|α|<π/2,β>0,0≤ρ<1,and letf(z)=z+sum from n=2 to∞ a_nz~nbe analytic in the unit disc E={z:|z|<1}.Futher letJ(α,β,γ,ρ,f(z))=(e~ia(zf’(z)/f(z))-ρcosα)~1-2γ[(e~ia(zf’(z)/f(z)-ρcosα)~2+βcosae~ia(zf’(z)/f(z)(1+zf”(z)/f’(z)-zf’(z)/f(z))]~γ     

Finding Zeros of Analytic Functions: α Theory for Secant Type Methods

We present new results concerning the convergence of secant type methods with only conditions at a point. The radius of robustness of these methods is given, and we apply it to the study of the complexity of homotopy methods for approximating roots. In particular, we say how to use the secant type method to get an approximate zero relative to the Newton method.     

Stability of Functional Equations in Several Variables

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.     

Operators of Almost Hadamard Type and Hardy–Littlewood Operator in the Space of Entire Functions of Several Complex Variables

Mathematical Notes - Conditions (in particular, on the order of decrease of the coefficients) for the uniform Pringsheim convergence of double trigonometric series with rarely changing coefficients...     

Uniqueness Theorems for Meromorphic Mappings in Several Complex Variables into PN（c） with Two Families of Moving Targets

The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C)with two families of moving targets,and the results obtained improve some earlier work.     

On the Bloch Constant for Κ-Quasiconformal Mappings in Several Complex Variables

We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C ⁿ . The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C ⁿ such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least where C _n > 1 is a constant depending on n only, and as n→∞. Received June 24, 1998, Accepted January 14, 1999     

Fréchet-Valued Real Analytic Functions on Fréchet Spaces

The aim of this paper is to establish the equivalence between the real and topologically real analyticity of Fréchet-valued functions on Fréchet spaces. This is an extension of recent results of Bonet and Domanski [1, 2] to infinite dimension.Received February 19, 2002; in revised form June 25, 2002 Published online May 16, 2003     

λ-Divergence of the Fourier Series of Continuous Functions of Several Variables

In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices for which for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity such that its Fourier series is -divergent everywhere for any .     

One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

Ukrainian Mathematical Journal - We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform...     

On Some New Integral Inequalities for Functions in One and Two Variables

In this paper, we consider a bound on a general version of the integral inequalities for functions and also study the qualitative behavior of the solutions of certain classes of the hyperbolic partial delay differential equations under the integral inequalities.     

The Comparison Theorems of Kolmogorov Type on a Convolution Class of Functions

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Cesàro Means of Orthogonal Expansions in Several Variables

Cesàro (C,δ) means are studied for orthogonal expansions with respect to the weight function on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the (C,δ) kernel with δ>−1 and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesàro means and the projection operator on these domains.      

Fourier Method for an Over-Determined Elliptic System with Several Complex Variables

Two boundary value problems are investigated for an over-determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential difference between the case of one complex variable and that of several complex variables is revealed.     

P≠NP for the Reals with Various Analytic Functions

We show that non-deterministic machines in the sense of L. Blum, M. Shub, and S. Smale (1989, Bull. Amer. Math. Soc.21) defined over wide classes of real analytic structures are more powerful than the corresponding deterministic machines.     

Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ N

In this paper, by the Alexandrov-Serrin method of moving plane combined with integral inequalities, we prove some new Liouville type results for positive solution of semilinear elliptic system in the whole space ? ^N .     

On Certain Inequalities for Some Analytic Functions and Differential Subordinations

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