The purpose of the present paper is to introduce and investigate the function classes k-SP (alpha, beta) and k-UCV (alpha, beta) of analytic functions associated with conic regions in the open unit disk U, which gener...
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The purpose of the present paper is to introduce and investigate the function classes k-SP (alpha, beta) and k-UCV (alpha, beta) of analytic functions associated with conic regions in the open unit disk U, which generalize the function classes defined and studied in a series of earlier papers by Kanas et al. [11, 12, 13, 14]. In particular, we consider the extremal problems for each of the above-mentioned function classes. The Fekete-Szego problem is also considered for functions in the class k-SP(alpha, beta). Moreover, we investigate some mapping properties for each of the function classes k-SP(alpha, beta) and k-UCV(alpha, beta).
Let A be the class of functions f : f (z) = z + Sigma(infinity)(n=2) a(n)z(n), which are analytic in the open unit disc E. We use a linear operator closely related to the multiplier transformation to introduce and inv...
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Let A be the class of functions f : f (z) = z + Sigma(infinity)(n=2) a(n)z(n), which are analytic in the open unit disc E. We use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of A which map E onto a generalized form of the conic domain. Several properties of these classes including some inclusion relations, convolution and other class preserving operators are studied. In particular, we derive many known and new results as special cases. Applications of some results are also given. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper, we find the necessary and sufficient conditions for functions zF(a, b;c;z) in the generalized class of beta uniformly starlike and beta uniformly convex functions of order alpha and also consequences of...
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In this paper, we find the necessary and sufficient conditions for functions zF(a, b;c;z) in the generalized class of beta uniformly starlike and beta uniformly convex functions of order alpha and also consequences of the results are pointed out. (C) 2010 Elsevier Ltd. All rights reserved.
Applying the coefficient inequalities of functions f(z) belonging to the subclasses M/D (alpha, beta) and N D(alpha,beta) of certain analytic functions in the open unit disk U, two subclasses MD* (alpha, beta) and N D...
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Applying the coefficient inequalities of functions f(z) belonging to the subclasses M/D (alpha, beta) and N D(alpha,beta) of certain analytic functions in the open unit disk U, two subclasses MD* (alpha, beta) and N D* (alpha, beta) are introduced. The object of the present paper is to derive some convolution properties of functions f(z) in the classes M D*(alpha, beta) and N D* (alpha,beta). (C) 2006 Elsevier Inc. All rights reserved.
In this paper the authors prove some properties for two general integral operators on the classes beta - UCV(alpha) and beta - s(p)(alpha). (C) 2010 Elsevier Ltd. All rights reserved.
In this paper the authors prove some properties for two general integral operators on the classes beta - UCV(alpha) and beta - s(p)(alpha). (C) 2010 Elsevier Ltd. All rights reserved.
We define the generalized Dziok-Srivastava operator for harmonic functions and introduce a new subclass of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. We inv...
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We define the generalized Dziok-Srivastava operator for harmonic functions and introduce a new subclass of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.
The object of this paper is to show some properties of functions belonging to a subclass M(A,B,b,α)(where b is a complex number with h (b) > 0,α >-1 and A,B are two arbitrary constants with(-1<B <A <1...
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The object of this paper is to show some properties of functions belonging to a subclass M(A,B,b,α)(where b is a complex number with h (b) > 0,α >-1 and A,B are two arbitrary constants with(-1functions are *** of close-to-convexity,starhkeness,convexity,convex linear combinations are ***,interesting operators could be obtained with some earlier results using standard methods.
For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product ( or convolution) with a generalized hypergeometric function, the authors investigate several m...
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For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product ( or convolution) with a generalized hypergeometric function, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, which are introduced here. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out.
We establish some conditions under which the differential subordination of the type p(z) + zp'(z)/p(z) < Q(z) yields p < q in U. functions Q and q are chosen so that they map the unit disk onto domains enclo...
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We establish some conditions under which the differential subordination of the type p(z) + zp'(z)/p(z) < Q(z) yields p < q in U. functions Q and q are chosen so that they map the unit disk onto domains enclosed by conic sections. Some applications of obtained results are given.
Let A be the class of analytic functions in the open unit disk U. Given 0 less than or equal to lambda < 1, let Omega(lambda) be the operator defined on A by (Omega(lambda)f) (z) = Gamma(2 - lambda)z(lambda)D(z)(la...
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Let A be the class of analytic functions in the open unit disk U. Given 0 less than or equal to lambda < 1, let Omega(lambda) be the operator defined on A by (Omega(lambda)f) (z) = Gamma(2 - lambda)z(lambda)D(z)(lambda) f(z), where D(z)(lambda)f is the fractional derivative of f of order lambda. A function f in A is said to be in the class SPlambda if Omega(lambda)f is a parabolic starlike function. In this paper, several basic properties and characteristics of the class SPlambda are investigated. These include subordination, inclusion, and growth theorems, class-preserving operators, Fekete-Szego problems, and sharp estimates for the first few coefficients of the inverse function. (C) 2000 Elsevier Science Ltd. All rights reserved.
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