Geometric Properties of Normalized Wright Functions

Mustafa, Nizami; Nezir, Veysel; Dutta, Hemen

doi:10.1007/978-3-319-99918-0_22

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…The answer to this question would ensure that it would be possible to obtain necessary and sufficient conditions on the parameters ρ and β such that the normalized forms of the Wright function belong to certain class of univalent functions, like starlike, convex or spirallike. Such kind of results would improve the existing results in the literature (see [20,21,22,23]). 2.…”

Section: The Radii Of Starlikeness and Convexity Of Normalized Wright...supporting

confidence: 69%

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Radii of starlikeness and convexity of Wright functions

Baricz,

Toklu,

Kadıoğlu

2017

Preprint

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In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.

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Section: The Radii Of Starlikeness and Convexity Of Normalized Wright...supporting

confidence: 69%

“…Special functions are indispensable in many branches of mathematics and applied mathematics. Geometric properties of some special functions were examined by many authors (see [1,2,3,4,5,7,8,9,10,11,20,21,22,23,24,25]). However, its origins can be traced to Brown [12] (see also [13,14]), to Kreyszig and Todd [19] and to Wilf [26].…”

Section: Introductionmentioning

confidence: 99%

Radii of starlikeness and convexity of Wright functions

Baricz,

Toklu,

Kadıoğlu

2017

Preprint

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“…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).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…Very recently, Cho et al [11] and Murugusundaramoorthy and Janani [22] (see also Porwal and Dixit [25]) introduced some characterization of generalized Bessel functions of first kind to be in certain subclasses of uniformly starlike and uniformly convex functions. Motivated by the new technique due to Mustafa [23], we determine some geometric properties of generalized Bessel function of the first type to be in S * (α, β) and K(α, β), followed by sufficient conditions for the familiar, modified and spherical Bessel functions as special cases.…”

Section: Introductionmentioning

confidence: 99%