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We introduce a new subclass of functions defined by multiplier differential operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient convolution conditions, distortion bounds and extreme points for these subclasses of functions. [ABSTRACT FROM AUTHOR]

A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions. [ABSTRACT FROM AUTHOR]

Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form $f=h+\overline{g}$, where h and g are analytic. In this paper we investigate some classes of univalent harmonic functions with varying coefficients related to Janowski functions. By using the extreme points theory we obtain necessary and sufficient convolution conditions, coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. The radii of starlikeness and convexity for these classes are also determined. [ABSTRACT FROM AUTHOR]

In this paper we investigate some generalizations of classes of harmonic functions. By using the extreme points theory we obtain coefficients estimates distortion theorems and integral mean inequalities in these classes of functions. [ABSTRACT FROM AUTHOR]

New classes of univalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. By using extreme points theory we also obtain coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. Radii of convexity and starlikeness of the classes are also considered. [ABSTRACT FROM AUTHOR]

In the present paper we define a class of products of multivalent close-to-star functions and determine the set of pairs [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], such that every function from the class maps the disk [InlineEquation not available: see fulltext.] onto a domain starlike with respect to the origin. Some consequences of the obtained result are also considered. MSC: 30C45, 30C50, 30C55. [ABSTRACT FROM AUTHOR]

Our objective in this paper is to consider some basic properties of the familiar Chebyshev polynomials in the theory of analytic functions. We investigate some basic useful characteristics for a class H ( t ) , t ∈ ( 1 / 2 , 1 ] , of functions f , with f ( 0 ) = 0 , f ′ ( 0 ) = 1 , analytic in the open unit disc U = { z : | z | < 1 } satisfying the condition that 1 + z f ″ ( z ) f ′ ( z ) ≺ H ( z , t ) = 1 1 − 2 t z + z 2 ( z ∈ U ) , where H ( z , t ) is the generating function of the second kind of Chebyshev polynomials. The Fekete–Szegö problem in the class is also solved. [ABSTRACT FROM AUTHOR]

In the paper we introduce the class of linear combinations of functions which are subordinated to a convex function. Some relationships between this class and the class of real-valued functions with bounded variation on [InlineEquation not available: see fulltext.] are obtained. Next, we define classes of functions associated with bounded Mocanu variation. By using the properties of multivalent prestarlike functions, we obtain various inclusion relationships between defined classes of functions. Some applications of the main results are also considered. MSC: 30C45, 30C50, 30C55. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate an interesting subclass of analytic univalent functions in the open unit disc on the complex plane. This class was introduced by Sokół [J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999) 111–116]. The class is strongly related to the class considered earlier by the authors of the present work in their paper [J. Dziok, R. K. Raina, J. Sokół, Certain results for a class of convex functions related to shell-like curve connected with Fibonacci Numbers, Comput. Math. Appl. 61 (2011) 2606–2613]. Apart from furnishing some genuine remarks, we present certain new results for the class of functions, and also mention some relevant cases for this function class. [Copyright &y& Elsevier]

The object of this paper is to give several strict inequalities associated with the operator Ip,nλ(a, b; c) (a, b ∈ R \ ℤ0- , p, n ∈ N = {1,2, …}, λ; > -p) defined by X.-L. Fu and M.-S. Liu, Some subclasses of analytic functions involving the generalized Noor integral operator [see 3]. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates some basic geometric properties for the class of functions analytic in the open unit disc (which is related to a shell-like curve and associated with Fibonacci numbers) satisfying the condition that where, the number is such that fulfils the golden section of the segment . Some relevant remarks and useful connections of the main results are also pointed out. [Copyright &y& Elsevier]

Abstract: Let , , denote the class of analytic functions in the unit disc normalized by and satisfying the condition The relations between and other classes geometrically defined are considered. The radii of convexity (starlikeness) of order are calculated. The same problem in the class of strongly starlike functions of order is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of meromorphic multivalent functions associated with Wright generalized hypergeometric function and obtain new results for this class by the application of Briot-Bouquet differential subordination. [ABSTRACT FROM AUTHOR]

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained. [ABSTRACT FROM AUTHOR]

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, RØnning, and Bharati et al. [ABSTRACT FROM AUTHOR]