Radius of starlikeness and hardy space of Mittag-Leffler functions

The main objective of this paper is to establish some sufficient conditions so that a class of normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness and k-uniform convexity are discussed for these functions. Some sufficient conditions are also derived so that these functions belong to the Hardy spaces Hp and H∞. Furthermore, the inclusion properties of some modified Mittag–Leffler-type functions are discussed. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.

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“…This leads to the known result ([52], Theorem 4.5). Hence, Theorem 8 generalizes the result given in [52].…”

Section: Hardy Space Of the Mittag-leffler-type Functionssupporting

confidence: 80%

“…This leads to the result given in ( [52], Theorem 4.6). Hence, Theorem 9 generalizes the corresponding known result ([52], Theorem 4.6).…”

Section: Hardy Space Of the Mittag-leffler-type Functionssupporting

confidence: 64%

Geometric Properties of a Certain Class of Mittag–Leffler-Type Functions

et al. 2022

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“…The technique of determining the radii of η−parabolic starlikeness of order ρ in the next theorem follows the ideas comes from [14]. The results of the next theorem are natural extensions of some recent results see [36], where the special case of γ = 1, η = 0 was considered. Theorem 2.5.…”

Section: 3mentioning

confidence: 78%

Radii problems for the generalized Mittag-Leffler functions

Prajapati

2019

Preprint

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In this paper our aim is to investigate the radii of η−uniformly convexity, α−convexity, η−parabolic starlikeness and strong starlikeness of order ρ of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

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“…Furthermore, Eenigenburg and Keogh determined some conditions on the convex, starlike and close-to-convex functions to belong to the Hardy space H p in [10]. On the other hand, the authors in [7,16,17,22,23,28,29] studied the Hardy space of some special functions (like Hypergeometric, Bessel, Struve, Lommel and Mittag-Leffler) and analytic function families.…”

Section: Introductionmentioning

confidence: 99%

On some geometric properties and Hardy class of <i>q</i>-Bessel functions

Aktaş

2020

AIMS Mathematics

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In this paper, we deal with some geometric properties including starlikeness and convexity of order α of Jackson's second and third q-Bessel functions which are natural extensions of classical Bessel function J ν . In additon, we determine some conditions on the parameters such that Jackson's second and third q-Bessel functions belong to the Hardy space and to the class of bounded analytic functions.where z ∈ C, ν > −1, q ∈ (0, 1) and (a; q) 0 = 1, (a; q) n = n k=1 1 − aq k−1 , (a, q) ∞ = k≥1 1 − aq k−1 .

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Radius of starlikeness and hardy space of Mittag-Leffler functions

Cited by 10 publications

References 10 publications

Geometric Properties of a Certain Class of Mittag–Leffler-Type Functions

Geometric Properties of a Certain Class of Mittag–Leffler-Type Functions

Radii problems for the generalized Mittag-Leffler functions

On some geometric properties and Hardy class of <i>q</i>-Bessel functions

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