Bi-Bazilevič functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials

El-Deeb, Sheza M.; Murugusundaramoorthy, G.; Alburaikan, Alhanouf

doi:10.22436/jmcs.024.03.05

Cited by 15 publications

(19 citation statements)

References 19 publications

(22 reference statements)

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“…Murugusundaramoorthy and El-Deeb [10], El-Deeb et al [4] and Srivastava et al [16] are defined the Mittag-Leffler-type Borel distribution as follows:…”

Section: Mittag-leffler Function and Borel Distributionmentioning

confidence: 99%

Some properties of analytical functions related to Borel distribution series

Niranjan¹,

Murthy²,

Reddy³

2022

J. Math. Computer Sci.

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“…Murugusundaramoorthy and El-Deeb [10], El-Deeb et al [4] and Srivastava et al [16] are defined the Mittag-Leffler-type Borel distribution as follows:…”

Section: Mittag-leffler Function and Borel Distributionmentioning

confidence: 99%

Some properties of analytical functions related to Borel distribution series

Niranjan¹,

Murthy²,

Reddy³

2022

J. Math. Computer Sci.

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“…We now recall the following Mittag-Leffler type Borel distribution that was studied by Murugusundaramoorthy and El-Deeb [2] (see also [1,3]):…”

Section: Remarkmentioning

confidence: 99%

“…We choose here to mention the works of El-Deeb et al [1], Murugusundaramoorthy and El-Deeb [2], Srivastava et al [3], and Wanas and Khuttar [4], in which use was made of the Borel distribution series, involving many different special functions and orthogonal polynomials, in their study of subclasses of normalized holomorphic functions in the open unit disk.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution

Srivástava

El-Deeb

2021

Symmetry

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In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series Bλ,α,β(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function Eα,β(z). Using the above-mentioned operator Bλ,α,β, we also introduce and study a class Mλ,α,βFη of holomorphic and univalent functions in the open unit disk Δ. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function pΨq(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.

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“…Motivated from all the above discussions and work from Khan et al [16], in which they introduced a class of analytic functions with Mittag-Leffler type Poisson distribution in the Janowski domain, analytic functions with Mittag-Leffler type Borel distribution [17], and the work in the articles [18,19], we now introduce a new class of analytic functions with the help of operator (2), as follows:…”

Section: Introductionmentioning

confidence: 99%

Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions

Ahmad¹,

Khan

Cotîrlǎ

2022

Symmetry

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The main purpose of this article is to introduce the new subclass of analytic functions whose coefficients are Borel distributions in the Janowski domain. Further, we investigate some useful number of properties such as Fekete–Szeg ö inequality, necessary and sufficient condition, growth and distortion approximations, convex linear combination, arithmetic mean, radii of close-to-convexity and starlikeness and partial sums, followed by some extremal functions for this defined class. The symmetry properties and other properties of the subclass of functions introduced in this paper can be studied as future research directions.

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Bi-Bazilevič functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials

Cited by 15 publications

References 19 publications

Some properties of analytical functions related to Borel distribution series

Some properties of analytical functions related to Borel distribution series

Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution

Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions

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