Top PDF Analytic Functions in General Analysis

Analytic Functions in General Analysis

Analytic Functions in General Analysis

sn expression of the foirm ments of Eo "'e shall deal with complex va:rit?bles» and shall always sup= pose that E is completeo •'·:\< f'' If for a value CJ~ ex© the terms of the series a[r]

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Majorization for Certain Analytic Functions

Majorization for Certain Analytic Functions

SPECIAL ISSUE FOR THE INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND ALGEBRA 29 JUNE - 02 JULY 2011, ISTANBUL TURKEY.. Majorization for Certain Analytic Functions.[r]

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1. Some applications of differential subordination to a general class 
                                of multivalently analytic functions
                                 involving a convolution structure

1. Some applications of differential subordination to a general class of multivalently analytic functions involving a convolution structure

volving the Hadamard product of two multivalently analytic functions and the pricipal of subordination. Several corollaries are deduced from the main results and their connections with known results are also pointed out. The concluding section exhibits relevant connections to some of the results presented here and those obtained in earlier works.

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Boundary value problems for periodic analytic functions

Boundary value problems for periodic analytic functions

In this paper boundary value problems for periodic analytic functions are discussed. We first introduce definitions of principal part and order at ±∞i for periodic analytic functions through detailed analysis. Then Riemann boundary value problems for periodic analytic functions with finite order at ±∞i are formulated. Based on those, by using the exponential conformal mapping, Riemann boundary value problems for periodic sectionally holomorphic functions with periodic closed and periodic quasi-closed contours as their jump curves are solved. The method that we use here has computational advantages compared with the tangent mapping one used in solving the classical problems. Several types of Hilbert boundary value problems on the real axis and the circumferences for periodic analytic functions are also solved.
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Neighborhoods of Certain Multivalently Analytic Functions

Neighborhoods of Certain Multivalently Analytic Functions

We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient bounds, distortion inequalities, and other interesting properties and characteristics for functions belonging to the classes introduced here.

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2 Fourier Analysis and Analytic Functions

2 Fourier Analysis and Analytic Functions

The previous section introduced the Hardy space of complex valued functions. In general, it is possible to extend the concept of Hardy spaces to functions taking values in arbitrary Banach spaces. To give a completely satisfactory definition of such spaces, one needs some results from the integration theory of functions with values in Banach spaces. Although this is a straight for- ward generalization of the standard integration of complex valued Lebesgue measurable functions, it would be out of the scope of our intentions here. However, for the case of functions with values in a separable or even a finite dimensional Hilbert spaces, almost the whole theory can be led back to the scalar case of the previous section. Therefore, we shall restrict ourselves to these cases. Later, we will be especially interested in the finite dimensional case, since this is the suitable framework for modeling linear systems with a finite number of inputs and outputs. Nevertheless, the basic definitions are given for the slightly more general case of separable Hilbert spaces.
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A Family of Convolution Operators for Multivalent Analytic Functions

A Family of Convolution Operators for Multivalent Analytic Functions

[3] N. E. Cho, O. S. Kwon and H. M. Srivastava. Inclusion relationships and argument prop- erties for certain subclasses of multivalent functions associated with a family of linear operators. Journal of Mathematical Analysis and Applications, 292:470–483, 2004. [4] J. Dziok and H. M. Srivastava. Classes of analytic functions associated with the general-

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A fixed point theorem for analytic functions

A fixed point theorem for analytic functions

ϕ HD( w , k ) ⊆ HD( w , k ) k > 0 . (2.3) The remarkable point w is called the Denjoy-Wolff point of ϕ. Relation (2.3) is a con- sequence of a geometric function-theoretic result known as Julia’s lemma. In case ϕ has a fixed point, but is not the identity or an elliptic disk automorphism, one can use Schwarz’s lemma in classical complex analysis to show that { ϕ [n] } tends to that fixed point, (which is also regarded as a constant function), uniformly on compact subsets of U . These facts show that if ϕ is not the identity, then it may have at most a fixed point in U . Good accounts on all the results summarized above can be found in [2, Section 2.3] and [4, Sections 4.4–5.3].
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Coefficient Estimates for a Certain General Subclass of Analytic and Bi Univalent Functions

Coefficient Estimates for a Certain General Subclass of Analytic and Bi Univalent Functions

f − w = − w a w + a − a w − a − a a + a w +  (1.2) A function f ∈  is said to be bi-univalent in  if both f and f − 1 are univalent in  . We denote by Σ the class of all bi-univalent functions in  . For a brief history and interesting examples of functions in the class Σ see [2] and the references therein.

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Growth Analysis of Functions Analytic in the Unit Polydisc

Growth Analysis of Functions Analytic in the Unit Polydisc

Abstract. In this paper we study some growth properties of composite func- tions analytic in the unit polydisc. Some results related to the generalised n variables based p-th Nevanlinna order (generalised n variables based p-th Nevanlinna lower order) and the generalised n variables based p-th Nevanlin- na relative order (generalised n variables based p-th Nevanlinna relative lower order) of an analytic function with respect to an entire function are established in this paper where n and p are any two positive integers. In fact in this paper we extend some results of [3] and [4].

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On Certain Sufficient Conditions for Analytic Univalent Functions

On Certain Sufficient Conditions for Analytic Univalent Functions

Abstract. In this paper, we introduce a new class B m l (α, δ) of functions which is defined by hyperge- ometric function and obtain its relations with some well-known subclasses of analytic univalent func- tions. Furthermore, as a special case, we show that convex functions of order 1/2 are also members of the family B m l (α, δ).

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Analytic functions of non Bazilevič type and starlikeness

Analytic functions of non Bazilevič type and starlikeness

Abstract. Two classes ¯ Ꮾ n (µ, α, λ) and ¯ ᏼ n (µ, α, λ) of analytic functions which are not Bazileviˇ c type in the open unit disk U are introduced. The object of the present paper is to consider the starlikeness of functions belonging to the classes ¯ Ꮾ n (µ, α, λ) and ¯ ᏼ n (µ, α, λ). 2000 Mathematics Subject Classification. 30C45.

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Interpolation by multipliers on certain spaces of analytic functions

Interpolation by multipliers on certain spaces of analytic functions

max{|f (z)| : z ∈ K}. Let G be an arbitrary bounded domain each point of which is a bounded point evaluation for a Hilbert space Ᏼ of functions analytic on G which contains the constant functions and admits multiplication by the independent variable z,M z , as a bounded operator. We denote such a Hilbert space by ( Ᏼ ,G). Also, we

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The radius of convexity of certain analytic functions II

The radius of convexity of certain analytic functions II

Univalent, analytic, starlike, convex, radius of starlikeness and radius of convexly.. 1980 MATHEMATICS SUBJECT CLASSIFICATION CODES.[r]

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A pointwise growth estimate for analytic functions in tubes

A pointwise growth estimate for analytic functions in tubes

Analytic Function in Tubes, Hardy H 2 Space, Cauchy Kernel and Integral, Foi- Laplace Integral.. 1980 MATHEMATICS SUBJECT CLASSIFICATION CODES: i..[r]

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On the radius of univalence of convex combinations of analytic functions

On the radius of univalence of convex combinations of analytic functions

ON THE RADIUS OF UNIVALENCE OF CONVEX COMBINATIONS OF ANALYTIC FUNCTIONS KHALIDA I.. ALOBOUDI and NAEELA ALDIHAN Mathematics Department Science College of Education for Girls Malaz, Sitt[r]

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New classification of analytic functions with negative coefficients

New classification of analytic functions with negative coefficients

Certain Classes of Multivalent Functions negative Coefficients, Bull.. Fractional Derivative Nihon Univ..[r]

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On certain classes of p valent analytic functions

On certain classes of p valent analytic functions

p-valent analytic function, Hadamard product, integral operator, multiplier transformation, p-valently convex of order 6.. 1991 AMS SUBJECT CLASSIFICATION CODE.[r]

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Analytic Functions Related with Mocanu Class

Analytic Functions Related with Mocanu Class

Lemma 1.4. [29] Let ε be a positive measure on [0, 1] . Let g be a complex-valued function defined on ∆×[0, 1] such that g (., t) is analytic in ∆ for each t ∈ [0, 1] and g (z, .) is ε-integrable on [0, 1] for all z ∈ ∆. In addition, suppose that Re g (z, t) > 0, g (−r, t) is real and Re {1/g (z, t)} ≥ 1/g (−r, t) for |z| ≤ r < 1 and t ∈ [0, 1] . If g (z) =

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Integral means of certain class of analytic functions

Integral means of certain class of analytic functions

Department of Mathematics Changsha Communications Institute Changsha, Hunan 410076 People’s Republic of China.. In this paper we discuss the following class of functions..[r]

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