Geometric Properties of the Products of Modified Bessel Functions of the First Kind

Mehrez, Khaled; Das, Sourav; Kumar, Anish

doi:10.1007/s40840-021-01082-2

Cited by 9 publications

(6 citation statements)

References 10 publications

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“…Setting A = α and B = β in (25), we obtain the Mittag-Leffler-type function as defined in (9), which is also known as the Le Roy-type Mittag-Leffler function [33]. Similarly, for A = α, B = β and γ = 1, G…”

Section: Remarkmentioning

confidence: 99%

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

et al. 2022

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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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Section: Remarkmentioning

confidence: 99%

“…Moreover, if h(z) is univalent in D, then g(z) ≺ h(z) if and only if g(0) = h(0) and g(D) ⊂ h(D). For more information on the various geometric properties involving subordination between analytic functions, we refer the reader to the earlier works [1,[5][6][7][8][9][10][11] and also to the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…For further details on geometric properties of analytic functions we refer to [5,[13][14][15][16] and references cited therein.…”

Section: Preliminariesmentioning

confidence: 99%

“…Problems for studying the geometric properties (including univalency, starlikeness or convexity) of family of analytic functions (in the unit disk) involving special functions have always been attracted by several researchers [2,9,10,15,16,20,21]. Mittag-Leffler functions are important special functions which play important role in fractional calculus, approximation theory and various branches of science and engineering.…”

Section: Motivationmentioning

confidence: 99%

On some geometric properties of the Le Roy-type Mittag-Leffler function

Mehrez¹,

Das²

2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, we consider the Le Roy-type Mittag-Leffler function. Our main focus is to establish some sufficient conditions so that the normalized Le-Roy type Mittag-Leffler function posses some geometric properties such as starlikeness, convexity, close-to-convexity (univalency) and uniformly convexity inside the unit disk. Using these results, geometric properties of the normalized Mittag-Leffler function are derived as application. Results obtained in this paper are new. Interesting consequences, corollaries and examples are provided to support that these results are better and improve several results available in the literature.

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“…Interested readers can find more information on the various geometric properties of certain analytic functions like the Wright function [5], generalized Bessel function [6][7][8], and Fox-Wright functions [9] in the listed references. For the geometric behavior of other special functions, one can refer to [10][11][12][13][14][15] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Further Geometric Properties of the Barnes–Mittag-Leffler Function

Alenazi,

Mehrez

2023

Axioms

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In this paper, we find sufficient conditions to be imposed on the parameters of a class of functions related to the Barnes–Mittag-Leffler function that allow us to conclude that it possesses certain geometric properties (such as starlikeness, uniformly starlike (convex), strongly starlike (convex), convexity, and close-to-convexity) in the unit disk. The key tools in some of our proofs are the monotonicity properties of a certain class of functions related to the gamma function.

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Geometric Properties of the Products of Modified Bessel Functions of the First Kind

Cited by 9 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

On some geometric properties of the Le Roy-type Mittag-Leffler function

Further Geometric Properties of the Barnes–Mittag-Leffler Function

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