uSIGMOID FUNCTION IN THE SPACE OF UNIVALENT lambda-PSEUDO STARLIKE FUNCTIONS

Abstract

In the present investigation, we obtain initial coefficients of λ− pseudo starlike functions related to sigmoid functions and the Fekete-Szegö coefficient functional |a 3 −µa 2 2 | for certain normalized analytic functions defined on the open unit disk. As an application of the main result,we pointed out the initial coefficients and Fekete-Szegö inequality for a subclasses of starlike functions related to sigmoid functions.

Initial Coefficients Estimates for Certain Generalized Class of Analytic Functions Involving Sigmoid Function

“…Using (2.9) and (2.10), the result is immediate.Incidentally, this result in (2.12) coincides with that of Murugusundaramoorthy and Janani[9].…”

“…By careful selection of the values for the parameters involves several interesting subclasses known and new are obtained (see [5,6,7,8,9,10,11,12,13]).…”

On Salagean type pseudo-starlike functions

“…The sigmoid function of the form h(z) = 1 1 + e −z is useful because it is differentiable. The sigmoid function has the following very important properties (see [3,4,8,9]):…”

Coefficient bounds for a class of univalent functions involving the modified Sigmoid function

“…More results can be found in Altinkaya andȮzkan [1], Mini and Keerthi [6] , Murugusundaramoorthy and Janani [7], Singh and Singh [10] and Wang and Wang [11] to mention just but a few. Definition 1.1.…”