Turkish Journal of Mathematics
Abstract
Let $T$ be the class of analytic functions in the open unit disc $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1.$ For $f(z)\in T,$ the Alexander integral operator $A_{-1}f(z),$ the Libera integral operator $L_{-1}f(z)$ and the Bernardi integral operator $B_{-1}f(z)$ were considered before. Using $A_{-1}f(z)$ and $L_{-1}f(z),$ a new integral operator $F_{\lambda}f(z)$ is considered. After discuss some properties of dominant for $F_{\lambda}f(z),$ another new integral operator $O_{-1}f(z)$ of $f(z)\in T$ is discussed. The object of the present paper is to discuss the dominant of new integral operators $F_{\lambda}f(z)$ and $O_{-1}f(z)$ concerning with some starlike functions and convex functions in $\mathbb{U}.$
DOI
10.3906/mat-2109-15
Keywords
Analytic function, Alexander integral operator, Libera integral operator, Bernardi integral operator, dominant, new integral operator
First Page
225
Last Page
241
Recommended Citation
GÜNEY, HATUN ÖZLEM and OWA, SHIGEYOSHI
(2022)
"New extension of Alexander and Libera integral operators,"
Turkish Journal of Mathematics: Vol. 46:
No.
1, Article 17.
https://doi.org/10.3906/mat-2109-15
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss1/17
