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Some Sandwich Theorems for Certain Analytic Functions Defined by Convolution

Some Sandwich Theorems for Certain Analytic Functions Defined by Convolution

Using the results of Miller and Mocanu [15], Bulboaca [4] considered certain classes of first order differential superordinations as well as superordination-preserving integral operators [5]. Ali et al. [1], have used the results of Bulboaca [4] to obtain sufficient conditions for normalized analytic functions to satisfy:

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Function theory for a beltrami algebra

Function theory for a beltrami algebra

analytic functions by means of systems of first order partial differential equations goes back at least to a paper of Picard in 1891 [I]... The solutions of that system.[r]

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Sandwich Theorems for Higher-Order Derivatives of Multivalent Analytic Functions Defined by Convolution Structure with Linear Operator

Sandwich Theorems for Higher-Order Derivatives of Multivalent Analytic Functions Defined by Convolution Structure with Linear Operator

The purpose of the present paper is to derive some applications of first order differential subordination and superordination results involving Hadamard product for multivalent analytic functions with linear operator defined in the open unit disk. These results are applied to obtain sandwich results.

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Multivalent functions and QK spaces

Multivalent functions and QK spaces

1. Introduction. For analytic univalent function f in the unit disk ∆ , Pommerenke [8] proved that f ∈ Ꮾ if and only if f ∈ BMOA, which easily implies a result of Baernstein II [4] about univalent Bloch functions: if g(z) ≠ 0 is an analytic univalent function in ∆ , then log g ∈ BMOA. We know that Pommerenke’s result mentioned above was generalized to Q p spaces for all p, 0 < p < ∞ , by Aulaskari et al. (cf. [2, Theorem 6.1]).

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Higher Order Finite Element Method for Inhomogeneous Axisymmetric Resonators

Higher Order Finite Element Method for Inhomogeneous Axisymmetric Resonators

In this work, we extend the higher-order FEM [19, 23] to improve the accuracy for the computation of inhomogeneous axisymmetric cavity problems. Although the higher-order FEM has been applied to 3-D problems, the new contribution of this work is that it develops and applies this method to BOR cavities. Both node- and edge-based elements are used to discretize the azimuthal and meridian components of the field. Numerical results are given to demonstrate the validity and efficiency of the higher-order FEM.

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Application of Srivastava-Attiya Operator to the Generalization of Mocanu Functions

Application of Srivastava-Attiya Operator to the Generalization of Mocanu Functions

Subordination of two functions f and g is denoted by f ≺ g and defined as f(z) = g(w(z)), where w(z) is schwarz function in f . Let S, S ∗ and C denotes the subclasses of χ of univalent functions, starlike functions and convex functions respectively. For 0 ≤ δ < 1, S ∗ (δ) and C(δ) are the subclasses of S of functions f satisfies;

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On A Subclass Of N-Uniformly Multivalent Functions Used By Incomplete Beta Function

On A Subclass Of N-Uniformly Multivalent Functions Used By Incomplete Beta Function

Key words and phrases : Analytic functions , Multivalent functions , Coefficient estimate, Distortion theorem, Starlike functions , Convex functions, Close-to-close functions, [r]

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Application of quasi-subordination for certain subclasses of bi-univalent functions of complex order

Application of quasi-subordination for certain subclasses of bi-univalent functions of complex order

A function f ∈ A is said to be bi-univalent in ∆ if both f and f −1 are univalent in ∆. Let Σ denote the class of bi- univalent functions in ∆ given by (1.1). For a brief his- tory and interesting examples in the class Σ, see [25] (see also [5], [6], [13], [16]). Furthermore, judging by the re- markable flood of papers on the subject (see, for example, [11], [23] and [24]). Not much is known about the bounds on the general coefficient |a n | . In the literature, there are

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The growth and approximation for an analytic function represented by Laplace–Stieltjes transforms with generalized order converging in the half plane

The growth and approximation for an analytic function represented by Laplace–Stieltjes transforms with generalized order converging in the half plane

In 1963, Yu [26] first proved the Valiron–Knopp–Bohr formula of the associated abscis- sas of bounded convergence, absolute convergence, and uniform convergence of Laplace– Stieltjes transform. Moreover, Yu [26] also estimated the growth of the maximal molecule M u (σ , F), the maximal term μ(σ, F), by introducing the concepts of the order of F(s), and

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Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

some geometric characterizations; such as univalent, starlike and bounded turning are studied. Our main tool is based on the Jack Lemma. It has proven that if (A) : A(U ) → A(U ). For future work, one can use the new operator to define new classes of analytic functions. Furthermore, for further investigations, one can study the subordination and superordination idea by employing the above integral. Additionally, it can be studied the connection between closed ideals of a Banach algebra together with closed invariant subspaces of the operator DA[f ].

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Method for Solving the Differential Problem Related to Sine and Cosine Functions

Method for Solving the Differential Problem Related to Sine and Cosine Functions

In calculus and engineering mathematics courses, finding f ( n ) ( c ) ( the n -th order derivative value of function f ( x ) at x  c ), in general, necessary goes through two procedures: Evaluating f ( n ) ( x ) ( the n -th order derivative of

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Sufficient conditions for starlikeness of reciprocal order

Sufficient conditions for starlikeness of reciprocal order

The object of the present paper is to derive certain sufficient conditions for starlikeness of reciprocal order of analytic functions in the open unit disk.. 2010 Mathematics Subject Cla[r]

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Strong boundedness of analytic functions in tubes

Strong boundedness of analytic functions in tubes

Analytic Function in Tube, Strong Boundedness, Tempered Distribos isibutional Boundary Value.. AMSMOS SUBJECT CLASSIFICATION 1970 CODES.[r]

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A fixed point theorem for analytic functions

A fixed point theorem for analytic functions

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 fi[r]

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On Partial Sums of Analytic Univalent Functions

On Partial Sums of Analytic Univalent Functions

Shahrood and the second author by a grant of Young Researchers and Elite Club, Malard Branch, Islamic Azad University.. References.[r]

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Retraction Notice to "Differential Subordinations for Higher-Order Derivatives of Multivalent Analytic Functions Associated with Dziok-Srivastava Operator"

Retraction Notice to "Differential Subordinations for Higher-Order Derivatives of Multivalent Analytic Functions Associated with Dziok-Srivastava Operator"

For two functions f and g analytic in U , we say that the function f is subordinate to g, written f ≺ g or f (z) ≺ g(z)(z ∈ U), if there exists a Schwarz function w analytic in U with w(0) = 0 and |w(z)| < 1(z ∈ U ) such that f(z) = g(w(z)),(z ∈ U ). In particular, if the function g is univalent in U , then f ≺ g if and only if f (0) = g(0) and f (U ) ⊂ g(U ).

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Some basic properties of certain subclasses of meromorphically starlike functions

Some basic properties of certain subclasses of meromorphically starlike functions

By means of Lemma . and (.), we know that (.) holds true. Combining (.) and (.), we readily get the coefficient estimates asserted by Theorem .. Following the earlier works (based upon the familiar concept of neighborhood of ana- lytic functions) by Goodman [] and Ruscheweyh [], and (more recently) by Altintaş et al. [–], Cˇataş [], Cho et al. [], Liu and Srivastava [–], Frasin [], Keerthi et al. [], Srivastava et al. [] and Wang et al. []. Assuming that γ is given by (.) and the condition (.) of Lemma . holds true, we here introduce the δ-neighborhood of a function f ∈ of the form (.) by means of the following definition:
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Neighborhoods and partial sums of certain subclass of starlike functions

Neighborhoods and partial sums of certain subclass of starlike functions

Following the earlier works (based upon the familiar concept of a neighborhood of analytic functions) by Goodman [] and Ruscheweyh [], and (more recently) by Altintaş et al. [–], Cˇataş [], Frasin [], Keerthi et al. [] and Srivastava et al. [], we begin by introducing here the δ-neighborhood of a function f ∈ A m of the form (.) by means of

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On starlikeness and close to convexity of certain analytic
functions

On starlikeness and close to convexity of certain analytic functions

Let H(p(z), zp (z)) ≺ h(z) be a first-order differential subordination. Then a univa- lent function q(z) is called its dominant if p(z) ≺ q(z) for all analytic functions p(z) that satisfy the differential subordination. A dominant ¯ q(z) is called the best dominant if ¯ q(z) ≺ q(z) for all dominants q(z). For the general theory of first-order differential subordination and its applications, we refer to [3].

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Existence Theorems for First Order Equations on Time Scales with  Carathéodory Functions

Existence Theorems for First Order Equations on Time Scales with Carathéodory Functions

Some papers treat the existence of solutions to systems of first-order equations on time scales. Existence results are obtained in 6, 7 under hypothesis different from ours. However, some particular cases obtained in 7 are corollaries of our existence result for problem 1.1. Also, our existence results treat the case where the right members in 1.1 and 1.2 are Δ- Carath´eodory functions which are more general than continuous functions used for systems studied in 6, 7. Let us mention that existence of extremal solutions for infinite systems of first-order equations of time scale with Δ-Carath´eodory functions is established in 8.
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