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B. A. Frasin

Publications and source records attributed to B. A. Frasin.

5 recordsLinked to original sources
arXiv2020

Uniformly convex spiral functions and uniformly spirallike function associated with Pascal distribution series

The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes SP_{p}(α,\b{eta}) and UCV_{p}(α,\b{eta}) of uniformly spirallike functions. Further, we consider properties of a special function related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

math.CV↗
arXiv2019

An application of generalized Bessel functions on subclasses of uniformly spirallike functions

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind $zu_{p}(z)$ to be in the classes $\mathcal{SP}_{p}(α,β)$ and $\mathcal{UCSP}(α,β)$ of uniformly spirallike functions and also give necessary and sufficient conditions for $z(2-u_{p}(z))$ to be in the above classes. Furthermore, we give necessary and sufficient conditions for $\mathcal{I}(κ,c)f$ \ to be in $\mathcal{UCSPT}(α,β)$ provided that the function $f$ is in the class $\mathcal{R}^{τ}(A,B)$. Finally, we give conditions for the integral operator $\mathcal{G(}κ,c,z\mathcal{)=}% \int_{0}^{z}(2-u_{p}(t))dt$ to be in the class $\mathcal{UCSPT}(α,β).$ Several corollaries and consequences of the main results are also considered.

math.CV↗
arXiv2019

On certain subclasses of analytic functions associated with Poisson distribution series

In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series $\mathcal{K}(m,z)=z+\sum_{n=2}^\infty \frac{m^{n-1}}{(n-1)!}e^{-m}z^{n}$ belonging to the subclasses $\mathcal{S}(k,λ)$ and $\mathcal{C}(k,λ)$ of analytic functions with negative coefficients. Further, we consider the integral operator $\mathcal{G}(m,z) = \int_0^z \frac{\mathcal{F}(m,ζ)}ζ dζ$ belonging to the above classes.

math.CV↗
arXiv2018

Starlikeness and convexity of integral operators involving Mittag-Leffler functions

In this paper, we shall find the order of starlikeness and convexity for integral operators \begin{equation*} \mathbb{F}_{α_{j},β_{j},λ_{j},ζ}(z)=\left\{ ζ\int\limits_{0}^{z}t^{ζ-1}\prod_{j=1}^{n}\left( \frac{\mathbb{E} _{α_{j},β_{j}}(t)}{t}\right) ^{1/λ_{j}}dt\right\} ^{1/ζ}, \end{equation*} where the functions $\mathbb{E}_{α_{j},β_{j}}$ are the normalized Mittag-Leffler functions.

math.CV↗