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Generalized operator for Alexander integral operator

Authors :
Güney H. Özlem
Owa Shigeyoshi
Source :
Acta Universitatis Sapientiae: Mathematica, Vol 12, Iss 2, Pp 294-306 (2020)
Publication Year :
2020
Publisher :
Scientia Publishing House, 2020.

Abstract

Let Tn be the class of functions f which are defined by a power series f(z)=z+an+1zn+1+an2zn+2+…f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots for every z in the closed unit disc 𝕌¯\bar {\mathbb{U}}. With m different boundary points zs, (s = 1,2,...,m), we consider αm ∈ eiβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass Bn(αm,β,ρ; j, λ) of Tn is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in Bn(αm,β,ρ; j, λ).

Details

Language :
English
ISSN :
20667752 and 20200021
Volume :
12
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Acta Universitatis Sapientiae: Mathematica
Publication Type :
Academic Journal
Accession number :
edsdoj.0f70f9e82f5415d80469b310831bfbf
Document Type :
article
Full Text :
https://doi.org/10.2478/ausm-2020-0021