Geometric Properties of the Four Parameters Wright Function

Das, Sourav; Mehrez, Khaled

doi:10.3103/s1068362322010058

Cited by 2 publications

(1 citation statement)

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“…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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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: Introductionmentioning

confidence: 99%

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

et al. 2022

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Further Geometric Properties of the Barnes–Mittag-Leffler Function

Alenazi,

Mehrez

2023

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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 Four Parameters Wright Function

Cited by 2 publications

References 19 publications

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

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

Further Geometric Properties of the Barnes–Mittag-Leffler Function

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