which are analytic in the open unit disk U {z : z ∈ C and |z| < 1} and S denote the subclass ofA that are univalent in U. A function f z inA is said to be in class S∗ of starlike functions of order zero in U, if R zf ′ z /f z > 0 for z ∈ U. Let K denote the class of all functions f ∈ A that are convex. Further, f is convex if and only if zf ′ z is star-like. A function f ∈ A is said to be close...

AbstractIn this paper, we introduce a new class K(α, β) of uniformly convex functions defined by a certain fractional calculus operator. The class has interesting subclasses like β-uniformly starlike, βuniformly convex and β-uniformly pre-starlike functions. Properties like coefficient estimates, growth and distortion theorems, modified Hadamard product, inclusion property, extreme points, clos...

In this paper we establish some results concerning the partial sums of meromorphic p-valent starlike functions and meromorphic p-valent convex functions.

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator. Inclusion relationships for these subclasses are established. Also, we introduce some integral-preserving properties. Moreover, connections of the results presented here with those obtained in earlier works are poi...

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...