University of MaraghehSahand Communications in Mathematical Analysis2322-580719420221001Convex and Starlike Functions Defined on the Subclass of the Class of the Univalent Functions $S$ with Order $2^{-r}$10911669665010.22130/scma.2022.541789.1010ENİsmetYıldızFaculty of Science and Arts, Department of Mathematics, Düzce University, Düzce, Turkey.OyaMertFaculty of Science and Arts, Department of Mathematics, Tekirdağ Namık Kemal University, Tekirdağ, Turkey.0000-0002-8791-3341AlaattinAkyarFaculty of Science and Arts, Department of Mathematics, Düzce University, Düzce, Turkey.Journal Article20211029In this paper, some conditions have been improved so that the function $g(z)$ is defined as $g(z)=1+\sum_{k\ge 2}^{\infty}a_{n+k}z^{n+k}$, which is analytic in unit disk $U$, can be in more specific subclasses of the $S$ class, which is the most fundamental type of univalent function. It is analyzed some characteristics of starlike and convex functions of order $2^{-r}$.https://scma.maragheh.ac.ir/article_696650_dcf8eb7e6811fa9ee0ae9935133f9794.pdf