A New Subclass of Analytic Functions Related to Mittag-Leffler Type Poisson Distribution Series

Abstract

The object of this work is to an innovation of a class k − U ~ S T s ℏ , υ , τ , ι , ς in Y with negative coefficients, further determining coefficient estimates, neighborhoods, partial sums, convexity, and compactness of this specified class.

On a Certain Subclass of Analytic Functions Defined by Touchard Polynomials

“…As a result of De Branges' study [1], the classic Bieberbach problem is successfully solved by applying a generalized hypergeometric function. Several types of special functions, including generalized hypergeometric Gaussian functions (see [2][3][4]) and Gegenbauer polynomials, (see [5]) have been studied extensively.…”

Applications of Mittag-Leffer Type Poisson Distribution to a Subclass of Analytic Functions Involving Conic-Type Regions

“…where E α;β ðψÞ is given by (28). It is worthy to note that the Mittag-Leffer type Poisson distribution is a generalization of Poisson distribution.…”

“…Furtheremore, Bajpai [27] also studied and obtain some necessary and sufficient conditions for this distribution series. Very recently, using the Mittag-Leffer type Poisson distribution series, Alessa et al [28] defined the convolution operator as…”

“…The sufficient ways were innovated for certain subclasses of starlike and convex functions involving these special functions (see for example [26,[29][30][31][32]). Motivated by the abovementioned works and from the work of Alessa et al [28], in this article, by mean of certain convolution operator for Mittag-Leffer type Poisson distribution, we shall define a new subclass of starlike functions involving both the conic-type regions and the Janowski functions. We then obtain some interesting properties for this newly defined function class including for example necessary and sufficient condition, convex combination, growth and distortion bounds, Fekete-Szegö inequality, and partial sums.…”

Study on Certain Subclass of Analytic Functions Involving Mittag-Leffler Function

“…, and E 3 = 1/2½e w 1/3 + 2e −ð1/3Þ cos ðð ffiffi ffi 3 p /2Þw 1/3 Þ: The Mittag-Leffler function arises naturally in the solution of fractional-order differential and integral equations and especially in the investigations of fractional generalization of kinetic equation, random walks, Levy flights, and super diffusive transport and in the study of complex systems. Several properties of Mittag-Leffler function and generalized Mittag-Leffler function can be found, e.g., in [9][10][11][12][13][14][15][16]. Observe that Mittag-Leffler function E υ,τ ðwÞ does not belong to the family A: Thus, it is natural to consider the following normalization of Mittag-Leffler functions as below:…”