Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we t...
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Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.
In this paper, we consider certain differential inequalities and first order differential subordinations. As their applications, we obtain some sufficient conditions for univalence, which generalize and refine some pr...
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In this paper, we consider certain differential inequalities and first order differential subordinations. As their applications, we obtain some sufficient conditions for univalence, which generalize and refine some previous results.
Let T-n(A, B, alpha) denote the class of functions of the form: f(z) = z + Sigma(infinity)(k=n+1) a(k)z(k) (n is an element of N = {1, 2, 3, ... }), which are analytic in the open unit disk U and satisfy the following...
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Let T-n(A, B, alpha) denote the class of functions of the form: f(z) = z + Sigma(infinity)(k=n+1) a(k)z(k) (n is an element of N = {1, 2, 3, ... }), which are analytic in the open unit disk U and satisfy the following subordination condition: f'(z) + alpha zf ''(z) < 1 + Az/1 + Bz (z is an element of U;-1 <= B < 1;B < A;alpha > 0). In this paper, we find the sharp lower bound on |z| = r < 1 for the functional Re{f'(z) + alpha zf ''(z)} over the class: T-n(A, B, 0) = { f(z) = z + Sigma(infinity)(k=n+1) a(k)z(k) f'(z) < 1 + Az/1 + Bz (n is an element of N = {1, 2, 3, ... };z is an element of U)}. By applying this result, several interesting consequences are given. (C) 2009 Elsevier Inc. All rights reserved.
Let q be analytic in the open unit disk U with q(0) = 1 and q(z) not equal 0 (z is an element of U). By using the method of differential subordinations, we derive certain conditions involving q and zq' under which...
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Let q be analytic in the open unit disk U with q(0) = 1 and q(z) not equal 0 (z is an element of U). By using the method of differential subordinations, we derive certain conditions involving q and zq' under which the functions q satisfy the following two-sided inequality: alpha(2)pi/2 < argq(z) alpha(1)pi/2 (z is an element of U) for some alpha(1) and alpha(2) (0 < alpha(1), alpha(2) <= 1). Several interesting consequences of the main results are also given. All these results presented here are sharp. (C) 2010 Elsevier Ltd. All rights reserved.
The author aims at finding certain conditions on the parameters a, b and c such that the normalized Gaussian hypergeometric function zF(a, b;c;z) given by F (a, b;c;z) = Sigma(infinity)(n=0) (a)(n)(b)(n)/(c)(n)(1)(n) ...
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The author aims at finding certain conditions on the parameters a, b and c such that the normalized Gaussian hypergeometric function zF(a, b;c;z) given by F (a, b;c;z) = Sigma(infinity)(n=0) (a)(n)(b)(n)/(c)(n)(1)(n) z(n), vertical bar z vertical bar < 1, is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, the generalized polylogarithm phi p, q(a, b, z), which is a particular representation of generalized hypergeometric functions, is considered. Conditions on the parameters a, b, p and q are found such th...
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In this paper, the generalized polylogarithm phi p, q(a, b, z), which is a particular representation of generalized hypergeometric functions, is considered. Conditions on the parameters a, b, p and q are found such that the normalized form of these generalized polylogarithms has certain geometric properties such as close-to-convexity, starlikeness and convexity in the open unit disc . Results for the Alexander transform of these generalized polylogarithm are also obtained.
In this paper, we introduce and study some new subclasses of p-valently starlike, p-valently convex, p-valently close-to-convex and p-valently quasi-convexfunctions which are defined by means of a certain class of in...
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In this paper, we introduce and study some new subclasses of p-valently starlike, p-valently convex, p-valently close-to-convex and p-valently quasi-convexfunctions which are defined by means of a certain class of integral operators. Several inclusion relationships for these p-valently analytic function classes are established and an integral operator associated with the functions in these subclasses is discussed.
The familiar Salagean operator is used here to define a new subclass of analytic and univalent functions in the open unit disk U. In this note we obtain some sufficient conditions for functions belonging to this class...
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The familiar Salagean operator is used here to define a new subclass of analytic and univalent functions in the open unit disk U. In this note we obtain some sufficient conditions for functions belonging to this class and mention few important consequences of our main results.
The purpose of the present article is to establish two theorems for a class of analytic univalent functions defined in the open unit disk. The results are proved by using techniques involving the principle of differen...
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The purpose of the present article is to establish two theorems for a class of analytic univalent functions defined in the open unit disk. The results are proved by using techniques involving the principle of differential subordination. Connections of these theorems with Bazilevic functions are considered and the main results are applied to obtain sufficient conditions for analytic functions to be starlike and close-to-convex.
Some results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescr...
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Some results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescribed radial growth.
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