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Search Results (5)

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Keywords = Miller-Ross-type Poisson distribution

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17 pages, 332 KiB  
Article
Starlike Functions of the Miller–Ross-Type Poisson Distribution in the Janowski Domain
by Gangadharan Murugusundaramoorthy, Hatun Özlem Güney and Daniel Breaz
Mathematics 2024, 12(6), 795; https://doi.org/10.3390/math12060795 - 8 Mar 2024
Cited by 3 | Viewed by 1094
Abstract
In this paper, considering the various important applications of Miller–Ross functions in the fields of applied sciences, we introduced a new class of analytic functions f, utilizing the concept of Miller–Ross functions in the region of the Janowski domain. Furthermore, we obtained [...] Read more.
In this paper, considering the various important applications of Miller–Ross functions in the fields of applied sciences, we introduced a new class of analytic functions f, utilizing the concept of Miller–Ross functions in the region of the Janowski domain. Furthermore, we obtained initial coefficients of Taylor series expansion of f, coefficient inequalities for f−1 and the Fekete–Szegö problem. We also covered some key geometric properties for functions f in this newly formed class, such as the necessary and sufficient condition, convex combination, sequential subordination and partial sum findings. Full article
10 pages, 293 KiB  
Article
On Miller–Ross-Type Poisson Distribution Series
by Basem Aref Frasin and Luminiţa-Ioana Cotîrlă
Mathematics 2023, 11(18), 3989; https://doi.org/10.3390/math11183989 - 20 Sep 2023
Cited by 2 | Viewed by 1380
Abstract
The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes ST*(γ,β) and KT(γ,β) of analytic functions [...] Read more.
The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes ST*(γ,β) and KT(γ,β) of analytic functions with negative coefficients. Furthermore, we investigate several inclusion properties of the class Yσ(V,W) associated of the operator Iα,cε defined by this distribution. We also take into consideration an integral operator connected to series of Miller–Ross-type Poisson distributions. Special cases of the main results are also considered. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
14 pages, 337 KiB  
Article
Sakaguchi Type Starlike Functions Related with Miller-Ross-Type Poisson Distribution in Janowski Domain
by Sheza M. El-Deeb, Asma Alharbi and Gangadharan Murugusundaramoorthy
Mathematics 2023, 11(13), 2918; https://doi.org/10.3390/math11132918 - 29 Jun 2023
Viewed by 1232
Abstract
In this research, using the Poisson-type Miller-Ross distribution, we introduce new subclasses Sakaguchi type of star functions with respect to symmetric and conjugate points and discusses their characteristic properties and coefficient estimates. Furthermore, we proved that the class is closed by an integral [...] Read more.
In this research, using the Poisson-type Miller-Ross distribution, we introduce new subclasses Sakaguchi type of star functions with respect to symmetric and conjugate points and discusses their characteristic properties and coefficient estimates. Furthermore, we proved that the class is closed by an integral transformation. In addition, we pointed out some new subclasses and listed their geometric properties according to specializing in parameters that are new and no longer studied in conjunction with a Miller-Ross Poisson distribution. Full article
12 pages, 321 KiB  
Article
Bell Distribution Series Defined on Subclasses of Bi-Univalent Functions That Are Subordinate to Horadam Polynomials
by Ibtisam Aldawish, Basem Frasin and Ala Amourah
Axioms 2023, 12(4), 362; https://doi.org/10.3390/axioms12040362 - 10 Apr 2023
Cited by 3 | Viewed by 1448
Abstract
Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson distribution, Borel distribution, the Mittag-Leffler-type Borel distribution, Miller–Ross-Type Poisson Distribution. In the present paper, by making use of the Bell [...] Read more.
Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson distribution, Borel distribution, the Mittag-Leffler-type Borel distribution, Miller–Ross-Type Poisson Distribution. In the present paper, by making use of the Bell distribution, we introduce and investigate a new family GΣt(x,p,q,λ,β,γ) of normalized bi-univalent functions in the open unit disk U, which are associated with the Horadam polynomials and estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to this class. Furthermore, we establish the Fekete–Szegö inequality for functions in the family GΣt(x,p,q,λ,β,γ). After specializing the parameters used in our main results, a number of new results are demonstrated to follow. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory II)
10 pages, 298 KiB  
Article
An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials
by Ala Amourah, Basem Aref Frasin and Tamer M. Seoudy
Mathematics 2022, 10(14), 2462; https://doi.org/10.3390/math10142462 - 15 Jul 2022
Cited by 28 | Viewed by 1979
Abstract
The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each [...] Read more.
The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each of these bi-univalent function classes, we have derived and explored estimates of the Taylor coefficients a2 and a3 and Fekete-Szegö functional problems for functions belonging to these new subclasses. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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