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DIFFERENTIAL SUBORDINATION AND STARLIKENESS OF ANALYTIC FUNCTIONS
"... Abstract. In the present paper by using the method of differential subordination we aim to prove some classical results in univalent function theory. In particular we give some new sufficient condition for an analytic function to be starlike and convex in the unit disc U. Also by applying Ruschewey ..."
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Abstract. In the present paper by using the method of differential subordination we aim to prove some classical results in univalent function theory. In particular we give some new sufficient condition for an analytic function to be starlike and convex in the unit disc U. Also by applying
STARLIKENESS AND CONVEXITY CONDITIONS FOR CLASSES OF FUNCTIONS DEFINED BY SUBORDINATION
, 2004
"... Communicated by H. Silverman ABSTRACT. We consider the family P(1, b), b> 0, consisting of functions p analytic in the open unit disc U with the normalization p(0) = 1 which have the disc formulation p − 1  < b in U. Applying the subordination properties to certain choices of p using the fu ..."
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Communicated by H. Silverman ABSTRACT. We consider the family P(1, b), b> 0, consisting of functions p analytic in the open unit disc U with the normalization p(0) = 1 which have the disc formulation p − 1  < b in U. Applying the subordination properties to certain choices of p using
Differential Subordination Properties of Soko ́ lStankiewicz Starlike Functions
"... abstract. Let p(z) be an analytic function defined on the open unit disk D and p(0) = 1. Condition β in terms of complex numbers D and real E with −1 < E < 1 and D  ≤ 1 is determined such that 1 + βzp′(z) ≺ 1+Dz 1+Ez implies p(z) ≺ √1 + z. Furthermore, the expression 1 + βzp ′(z) p(z) an ..."
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abstract. Let p(z) be an analytic function defined on the open unit disk D and p(0) = 1. Condition β in terms of complex numbers D and real E with −1 < E < 1 and D  ≤ 1 is determined such that 1 + βzp′(z) ≺ 1+Dz 1+Ez implies p(z) ≺ √1 + z. Furthermore, the expression 1 + βzp ′(z) p
Test Starlike Functions for Approximation by Subordinate Polynomials
"... We construct a function f(z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f ∗ λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample t ..."
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We construct a function f(z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f ∗ λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample
DIFFERENTIAL INEQUALITIES AND CRITERIA FOR STARLIKE AND UNIVALENT FUNCTIONS
"... ABSTRACT. The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f sat ..."
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ABSTRACT. The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f
Subordination Criteria
, 2008
"... Applying Sǎlǎgean operator, for the class A of analytic functions f(z) in the open unit disk U which are normalized by f(0) = f ′ (0) − 1 = 0, the generalization of an analytic function to discuss the starlikeness is considered. Furthermore, from the subordination criteria for Janowski functions g ..."
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Applying Sǎlǎgean operator, for the class A of analytic functions f(z) in the open unit disk U which are normalized by f(0) = f ′ (0) − 1 = 0, the generalization of an analytic function to discuss the starlikeness is considered. Furthermore, from the subordination criteria for Janowski functions
Convolution and Differential Subordination for Multivalent Functions
, 2008
"... Abstract. The general classes of multivalent starlike, convex, closetoconvex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordin ..."
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Abstract. The general classes of multivalent starlike, convex, closetoconvex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential
Starlikeness and convexity of a class of analytic functions
 ID 38089, 8 pp. Received by the editors September
"... Let be the class of analytic functions in the unit disk that are normalized with f (0)= ..."
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Let be the class of analytic functions in the unit disk that are normalized with f (0)=
Results 1  10
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733