Geometric Properties of Normalized Wright Functions

Abstract

The purpose of the present paper is to investigate some characterizations for the Wright functions to be in the subclasses S˚pα, βq and Cpα, βq pα, β P r0, 1qq. Several sufficient conditions are obtained for the normalized Wright functions to be in these classes. Results obtained in this paper are new and their usefulness is put forth by several corollaries.

Necessary and Sufficient Conditions for Normalized Wright Functions to Be in Certain Classes of Analytic Functions

“…In recent years, several researchers have used the normalized Wright functions (see [30][31][32][33]) to obtain some necessary and sufficient conditions so that they are in certain classes of analytic functions with negative coefficients. Motivated with the aforementioned works, several sufficient and necessary conditions are provided in the present work for the normalized Wright functions Ψ (1) (γ, δ; z) and Ψ (2) (γ, δ; z) so that they are in classes SP p (σ, ν) and U CSP (σ, ν).…”

Certain Geometric Properties of Lommel and Hyper-Bessel Functions

“…Recently, many mathematicians study the geometric properties of special functions with different aspects. For details, we refer to [4][5][6][7][8][9]. Certain conditions for close-to-convexity of some special functions such as Bessel functions, q-Mittag-Leffler functions, Wright functions, and Dini functions have been determined by many mathematicians with different methods (for details, see [4,[10][11][12][13]).…”

Geometric properties of Wright function

“…The normalized Wright function W λ,µ was studied recently by the present author in [23] (see also [17]). Note that…”