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.

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

Geometric properties of mixed operator involving Ruscheweyh derivative and Salagean operator

"Operator theory is a magnificent tool for studying the geometric beha- viors of holomorphic functions in the open unit disk. Recently, a combination bet- ween two well known di erential operators, Ruscheweyh derivative and Salagean operator are suggested by Lupas in [10]. In this effort, we shall follow the same principle, to formulate a generalized di erential-difference operator. We deliver a new class of analytic functions containing the generalized operator. Applications are illustrated in the sequel concerning some di erential subordinations of the operator."

Applications of a Multiplier Transformation and Ruscheweyh Derivative for Obtaining New Strong Differential Subordinations

Here, we study strong differential subordinations for the extended new operator IRλ,lm defined by the Hadamard product of the extended multiplier transformation Im,λ,l and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions Anζ∗={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}, by IRλ,lm:Anζ∗→Anζ∗, IRλ,lmfz,ζ=Im,λ,l∗Rmfz,ζ.

A certain q-Ruscheweyh type derivative operator and its applications involving multivalent functions

In the present paper, by using the concept of convolution and q-calculus, we define a certain q-derivative (or q-difference) operator for analytic and multivalent (or p-valent) functions. This presumably new q-derivative operator is an extension of the known q-analogue of the Ruscheweyh derivative operator. We also give some interesting applications of this q-derivative operator for multivalent functions by using the method of differential subordination. Relevant connections with a number of earlier works on this subject are also pointed out.

Chebyshev Polynomials for Certain Subclass of Bazilevic Functions Associated with Ruscheweyh Derivative

In this paper, through the instrument of the well-known Chebyshev polynomials and subordination, we defined a family of functions, consisting of Bazilević functions of type α, involving the Ruscheweyh derivative operator. Also, we investigate coefficient bounds and Fekete-Szegö inequalities for this class.

Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

The main purpose of this manuscript is to find upper bounds for the second and third Taylor-Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Ruscheweyh derivative operator. Further, we point out certain special cases for our results.

The q-difference operator associated with the multivalent function bounded by conical sections

In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.