Convex family of meromorphically multivalent functions on connected sets
Abstract In this paper, by using a differential operator we have defined a new class of meromorphically multivalent functions. Also two useful subclasses of this class involving fixed points are investigated. Important properties of these classes like convex linear combination, coefficient estimates, convex family etc. are found.
Some Interesting Properties of a Subclass of Meromorphic Univalent Functions Defined by Hadamard Product
In the present paper, we define a new subclass ���(�, �, �, �) of meromorphic univalent with positive coefficients defined by Hadamard product in the punctured unit disk �∗. We obtain some interesting properties, like, coefficient estimates, extreme points, distortion theorem, partial sums, integral representation. 2014 Mathematic Subject Classification: 30C45
A new class of numerical sequences and its applications to sine and cosine series
First, it is proved that the class of classical quasi-monotone sequences is not comparable to the newly defined class of sequences of ‘rest bounded variation’. Considering this result, we prove three sample theorems for sequences of rest bounded variation, being analogues of the theorems proved earlier for monotone or quasi-monotone sequences. One of them gives a partial answer to a question raised by R. P. Boas Jr.