G. Murugusundaramoorthy

Starlike and convex functions of complex order involving the Dziok-Srivastava operator

Making use of Dziok-Srivastava operator we investigate starlike and convex functions of complex order defined by means of Hadamard product.

Subordination results for spiral-like functions associated with the Srivastava–Attiya operator

In this paper, making use of the generalized Srivastava–Attiya operator , we introduce a new subclass of spiral-like functions and discuss some subordination results for functions in this generalized function class. Furthermore, we mention some known and new results, which follow as special cases of our results.

Hypergeometric functions in the parabolic starlike and uniformly convex domains

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.

Coefficient Bounds for Certain Subclasses of Bi-Univalent Function

We introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients and for functions in these new subclasses. Also consequences of the results are pointed out.

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

Abstract In the present investigation we define a new class of meromorphic functions on the punctured unit disk Δ * : = { z ∈ ℂ : 0 | z | 1 } by making use of the generalized Dziok–Srivastava operator H m l [ α 1 ] . Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.

STARLIKENESS OF MULTIVALENT MEROMORPHIC HARMONIC FUNCTIONS

We give sufficient coefficient conditions for starlikeness of a class of complex-valued multivalent meromorphic harmonic and orientation preserving functions in outside of the unit disc. These coefficient conditions are also shown to be necessary if the coefficients of the analytic part of the harmonic functions are positive and the coefficients of the co-analytic part of the harmonic functions are negative. We then determine the extreme points, distortion bounds, convolution and convex combination conditions for these functions.

On certain subclasses of analytic functions associated with hypergeometric functions

Abstract In this paper, we find the necessary and sufficient conditions for functions z F ( a , b ; c ; z ) in the generalized class of β uniformly starlike and β uniformly convex functions of order α and also consequences of the results are pointed out.

Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class . In particular, we obtain integral means inequalities for the function that belongs to the class in the unit disc.

Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

Let 𝑓 𝑛 ∑ ( 𝑧 ) = 𝑧 + 𝑛 𝑘 = 2 𝑎 𝑘 𝑧 𝑘 be the sequence of partial sums of the analytic function ∑ 𝑓 ( 𝑧 ) = 𝑧 + ∞ 𝑘 = 2 𝑎 𝑘 𝑧 𝑘 . In this paper, we determine sharp lower bounds for ℜ { 𝑓 ( 𝑧 ) / 𝑓 𝑛 ( 𝑧 ) } , ℜ { 𝑓 𝑛 ( 𝑧 ) / 𝑓 ( 𝑧 ) } , ℜ { 𝑓  ( 𝑧 ) / 𝑓  𝑛 ( 𝑧 ) } , and ℜ { 𝑓  𝑛 ( 𝑧 ) / 𝑓  ( 𝑧 ) } . The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.

Subclasses of Starlike Functions Associated with Fractional -Calculus Operators

Making use of fractional -calculus operators, we introduce a new subclass of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in . Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in .