Neighborhoods for certain subclasses of multivalently analytic functions defined by using a differential operator

Neighborhoods of Certain Multivalently Analytic Functions

Serap Bulut Civil Aviation College, Kocaeli University, Arslanbey Campus, 41285 İzmit-Kocaeli, Turkey Correspondence should be addressed to Serap Bulut, [email protected] Received 28 March 2012; Accepted 16 May 2012 Academic Editor: Hernando Quevedo Copyright q 2012 Serap Bulut. This is an open access article distributed under the Creative Commons Attribution License, which permits unr...

On Certain Subclasses of Analytic Functions Defined by Differential Subordination

Some Subclasses of Analytic Functions Defined by Generalized Differential Operator

Let A denote the class of analytic functions in the open unit disk U = {z : |z| < 1} normalized by f(0) = f ′(0) − 1 = 0. In this paper, we introduce and study certain subclasses of analytic functions. Several inclusion relations of various subclasses of analytic functions, coefficient estimates , growth and distortion theorems, Hadamard Product, extreme points, integral means and inclusion pro...

Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Linear Operator

which are analytic in the open unit disk U {z ∈ C : |z| < 1}. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z if there exists an analytic function w in U with w 0 0 and |w z | < 1 for z ∈ U such that f z g w z . We denote by S∗, K, and C the subclasses of A consisting of all analytic functions which are, respectively, starlike, convex, and close-to-co...

On Certain Subclasses of Multivalent Functions with Negative Coefficients Defined by Using a Differential Operator

Making use of a differential operator the author investigate the various impartant properties and characteristics of the subclass Tj(n,m, p, q, α) (p, j,m ∈ N = {1, 2, . . .}, q, n ∈ N0 = N ∪ {0}, 0 ≤ α < p − q) of p-valently analytic functions with negative coefficients. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.