1,720,981 research outputs found
An Application of Pascal Distribution Series on Certain Analytic Functions Associated with Stirling Numbers and Sălăgean Operator
No full textIn the present paper, we will observe that the Sălăgean differential operator can be written in terms of Stirling numbers. Furthermore, we find a necessary and sufficient condition and inclusion relation for Pascal distribution series to be in the class ℙkλ,α of analytic functions with negative coefficients defined by the Sălăgean differential operator. Also, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered
Univalence criteria for general integral operator
Full text linkLet be the class of all analytic functions which are analytic
in the open unit disc $\mathcal{U=}\left\{ z:\left\vert z\right\ver
New conditions for Pascal distribution series to be in a certain class of analytic functions
No full textStudies of Sălăgean differential operator Dκ in connection with Stirling numbers are relatively new. In this paper, the differential operator Dκ involving Stirling numbers is considered. New necessary and sufficient conditions involving Stirling numbers for the series ϒθs(ς) written by the Pascal distribution are discussed for the subclass Tκ(ϵ,α). Also, we provide sufficient condition for the inclusion relation Iθs(Rϖ(E,D))⊂Tκ(ϵ,α). Further, we consider the properties of integral operator related to Pascal distribution series. New special cases as consequences of the main results are also obtained
Fekete-Szegö Inequality for Analytic and Biunivalent Functions Subordinate to Gegenbauer Polynomials
No full textIn the present paper, a subclass of analytic and biunivalent functions by means of Gegenbauer polynomials is introduced. Certain coefficients bound for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results
On Miller–Ross-Type Poisson Distribution Series
No full textThe 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
Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function
No full textRecently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller–Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler function Fα,βγ(z)=z+∑n=1∞Anzn+1, where An=ΓβΓα(n−1)+βγ and its sequence of partial sums (Fα,βγ(z))m(z)=z+∑n=1mAnzn+1. Several examples of the main results are also considered
Bi-Univalent Function Classes Defined by Imaginary Error Function and Bernoulli Polynomials
No full textIn recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined in U={ς∈C:|ς|<1}, characterized by Bernoulli polynomials associated with imaginary error functions. For functions belonging to these subclasses, we establish bounds for their initial coefficients. For these classes, we also tackle the Fekete–Szegö problem. Several new results are also obtained as special cases by specifying certain parameter values in the general findings
Majorization for Certain Classes of Analytic Functions Defined by Fournier–Ruscheweyh Integral Operator
No full textIn this paper, we introduce three new classes SkaM,N;μ,Rkaμ, and Tkaθ of analytic functions defined by Fournier–Ruscheweyh integral operator. For these classes, we investigate the majorization problem. Furthermore, a number of new results are shown to follow upon specializing the parameters involved in our main results
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