PARTIAL SUMS OF GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A GAUSSIAN HYPERGEOMETRIC FUNCTION
The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain classical orthogonal polynomials (deduced from some of the main results) exhibiting the usefulness of the results presented in this paper.
SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS DEFINED BY DZIOK-SRIVASTAVA OPERATOR WITH COMPLEX ORDER
In this paper we introduce a new class of harmonic univalent functions defined by the Dziok-Srivastava operator. Coefficient estimates, extreme points, distortion bounds and convex combination for functions belonging to this class are obtained and also for a class preserving the integral operator.
UNIVALENT HARMONIC FUNCTIONS
Harmonic functions, Dziok-Srivastava operator, Convolution, Integral operator, Distortion bounds, Neighborhood. Abstract: A necessary and sufficient coefficient is given for functions in a class of complex- valued harmonic univalent functions using the Dziok-Srivastava operator. Dis- tortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.