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.
Harmonic univalent functions associated with Wright's generalized hypergeometric functions
The purpose of this paper is to study certain harmonic univalent mappings involving the Wright's generalized hypergeometric functions. We investigate the usual characteristics associated with such harmonic mappings and also mention their validity conditions. As consequences of our main results, we deduce several results involving the generalized Mittag–Leffler function, the Bessel–Maitland function and the generalized hypergeometric function.
A CLASS OF MULTIVALENT ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS INVOLVING WRIGHT’S GENERALIZED HYPERGEOMETRIC FUNCTIONS
In this paper, a class of analytic functions with fixed argument of its coefficients involving Wright’s generalized hypergeometric function is defined with the help of subordination. The coefficient inequalities have been derived. Growth, distortion bounds and extreme points for functions belonging to the defined class have been investigated with consequent results.