Neighbourhoods of a Subclass of Uniformly Convex Functions
نویسندگان
چکیده
In this paper, we investigate the properties of neighbourhoods of functions for the classes U CV (α) and Sp(α). First we established an inclusion relationship between them and proved a necessary and sufficient condition interms of convolutions for a function f to be in Sp(α). Next we show that the class Sp(α) is closed under convolution with functions f (z) which are convex univalent. The results obtained in this which generalizes the results of Padmanabhan [8] and Ronning [9].
منابع مشابه
The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions
For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we definea subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative $mathrm{T}...
متن کاملOn a subclass of multivalent analytic functions associated with an extended fractional differintegral operator
Making use of an extended fractional differintegral operator ( introduced recently by Patel and Mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.
متن کاملA New Subclass of Uniformly Convex Functions and a Corresponding Subclass of Starlike Functions with Fixed Second Coefficient
Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely ma...
متن کاملA Subclass of Uniformly Convex Functions and a Corresponding Subclass of Starlike Functions with Fixed Second Coefficient Defined by Carlson and Shaffer Operator
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 ...
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کامل