We introduce a unified subclass of the function class Σ of biunivalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients | 2 | and | 3 | for functions in this subclass. In addition, many relevant connections with known or new results are pointed out.

Abstract. We investigate a family that connects various subclasses of functions convex in the unit disk. We also look at generalized sequences for this family.

In this article, a new subclass of harmonic mappings with restricted analytic part is introduced. Coefficient bounds, Fekete-Szego inequality and integral representation for functions in this subclass are established. Further closure of this class under convex combination is proved. Finally we obtain an upper bound for the Bloch's constant for functions in this class.

Abstract. Making use of the generalized hypergeometric functions, we introduced certain new subclasses of analytic functions defined by Dziok-Srivastava operator in the unit disc. The main object of the present paper is to investigate the various properties and characteristics of analytic functions belonging to the subclasses S n (l, m, λ , b, γ ) satisfying the inequalityis Dziok-Srivastava operator. Also let R n (l, m, λ , b, γ ) be an another subclass satisfying the inequalityis given by by Dziok-Srivastava [7]. Apart from deriving a set of coefficient bounds for each of these function classes, we establish several inclusion relationships involving the (n, δ )− negihborhoods of analytic functions with negative coefficients belonging to these subclasses. (2000): 30C45. Mathematics subject classification

In this paper, we define a new operator on the class of meromorphic functions and define a subclass using Hilbert space operator. Coefficient estimate, distortion bounds, extreme points, radii of starlikeness, and convexity are obtained.