Function Spaces, Fixed Points, Approximations, and Applications (original) (raw)

A study of a new subclass of multivalent analytic functions

saber.ula.ve

After introducing a new linear differential operator, we introduce and study certain new subclasses of analytic and multivalent functions in the open unit disk. Some inclusion relationships also discussed in particular with reference to an integral operator. key words. Analytic functions, Differential operator, Inclusion relationship AMS(MOS) subject classifications.

Some properties of certain class of multivalent analytic functions

In this paper we introduce a certain general class Φ β p (a, c, A, B) (β ≥ 0, a > 0, c > 0, −1 ≤ B < A ≤ 1, p ∈ N = {1, 2, ...}) of multivalent analytic functions in the open unit disc U = {z : |z| < 1} involving the linear operator Lp(a, c). The aim of the present paper is to investigate various properties and characteristics of this class by using the techniques of Briot-Bouquet differential subordination. Also we obtain coefficient estimates and maximization theorem concerning the coefficients.

On Certain Classes of Multivalent Analytic Functions

Journal of Mathematics and Statistics, 2010

Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent analytic functions in the open unit disk U was introduced. An application of this class was posed by using the fractional integral operator. The integral operator of multivalent functions was proposed and defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bounds established by using standard method. These results reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained the coefficient bounds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.

Some relations between certain classes of analytic functions

In the present paper we introduce and studied two subclasses of multivalent functions denoted by M λ p,n (γ;β ) and N λ p,n (μ,η;δ ) . Further, by giving specific values of the parameters of our main results, we will find some connection between these two classes, and moreover, several consequences of main results are also discussed.

Certain subclasses of multivalent analytic functions defined by multiplier transforms

Applied Mathematics and Computation, 2010

a b s t r a c t By making use of the principle of subordination between analytic functions and a family of multiplier transforms, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships, subordination and superordination properties, integral-preserving properties, argument estimates and convolution properties are proved. Crown j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c which are analytic and convex in U and satisfy the condition RðpðzÞÞ > 0 ðz 2 UÞ: