On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class k−STqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class k−STqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included.

Some Geometric Properties of Generalized Class of Meromorphic Functionsassocisted with Higher Ruscheweyh Derivatives

The applications of Ruscheweyh derivative are studied and discussed of class of meromorphic multivalent application. We get some interesting geometric properties, such as coefficient bound, Convex linear combination, growth and distortion bounds, radii of starlikenss , convexity and neighborhood property.

ON SOME SUBCLASSES OF HARMONIC MAPPINGS

Let ${\mathcal{P}}_{{\mathcal{H}}}^{0}(M)$ denote the class of normalised harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $\text{Re}\,(zh^{\prime \prime }(z))>-M+|zg^{\prime \prime }(z)|$, where $h^{\prime }(0)-1=0=g^{\prime }(0)$ and $M>0$. Let ${\mathcal{B}}_{{\mathcal{H}}}^{0}(M)$ denote the class of sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $|zh^{\prime \prime }(z)|\leq M-|zg^{\prime \prime }(z)|$, where $M>0$. We discuss the coefficient bound problem, the growth theorem for functions in the class ${\mathcal{P}}_{{\mathcal{H}}}^{0}(M)$ and a two-point distortion property for functions in the class ${\mathcal{B}}_{{\mathcal{H}}}^{0}(M)$.

Radius Constants for Functions with the Prescribed Coefficient Bounds

For an analytic univalent functionf(z)=z+∑n=2∞anznin the unit disk, it is well-known thatan≤nforn≥2. But the inequalityan≤ndoes not imply the univalence off. This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of orderα (0≤α<1) for functions with prescribed coefficient bound on the analytic part.

Certain new classes of meromorphic functions related with a convolution operator

Recently, Hussain [Hussain, Saqib (2010). Some applications of Miller-Mocanu lemma on certain classes of meromorphic functions, \textquotedblright Appl. Math. Comput.\textquotedblright , 216(2010), 3016-3021], introduced certain new classes of meromorphic functions using newly defined convolution operators. The purpose of present investigation is to extend the work of Hussain by considering some new classes of meromorphic functions. We derive some inclusion relationships, coefficient bound, integral representation and extreme point theorem.

A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution). A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also consider several applications of our main results to the generalized hypergeometric functions.

Subclass of harmonic univalent functions associated with Salagean derivative

In the present paper a new subclass of Harmonic univalent functions is defined using Salegaon derivative operator and several interesting properties like coefficient bound, distortion theorem are obtained.

Some uniformly starlike functions with varying arguments

In this paper two new subclasses of starlike functions that are analytic and normalized in the open unit disc with varying arguments is introduced. For functions in these classes we obtained coefficient bound, distortion results and the extreme points.