New Subclass of Convex Functions Concerning Infinite Cone
We introduce a new subclass of convex functions as follows:\[ \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\left|f'(z)-1\right|,\quad |z|<1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in t...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2024-03-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_709283_84739b66a34d93ea1b4d5887d2ebc69b.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823859373236027392 |
|---|---|
| author | Fatolah Hasanvand Shahram Najafzadeh Ali Ebadian |
| author_facet | Fatolah Hasanvand Shahram Najafzadeh Ali Ebadian |
| author_sort | Fatolah Hasanvand |
| collection | DOAJ |
| description | We introduce a new subclass of convex functions as follows:\[ \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\left|f'(z)-1\right|,\quad |z|<1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. Some properties of this particular class, including subordination relation, integral representation, the radius of convexity, rotation theorem, sharp coefficients estimate and Fekete-Szeg\"{o} inequality associated with the $k$-th root transform, are investigated. |
| format | Article |
| id | doaj-art-0b3ea09e16b94ca185e925aa994581aa |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-0b3ea09e16b94ca185e925aa994581aa2025-02-11T05:24:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-03-0121216717810.22130/scma.2023.2002626.1332709283New Subclass of Convex Functions Concerning Infinite ConeFatolah Hasanvand0Shahram Najafzadeh1Ali Ebadian2Department of Mathematics, Payame Noor University, P.O.Box 19395-3697 Tehran, Iran.Department of Mathematics, Payame Noor University, P.O.Box 19395-3697 Tehran, Iran.Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.We introduce a new subclass of convex functions as follows:\[ \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\left|f'(z)-1\right|,\quad |z|<1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. Some properties of this particular class, including subordination relation, integral representation, the radius of convexity, rotation theorem, sharp coefficients estimate and Fekete-Szeg\"{o} inequality associated with the $k$-th root transform, are investigated.https://scma.maragheh.ac.ir/article_709283_84739b66a34d93ea1b4d5887d2ebc69b.pdfunivalentconvexitysubordinationfekete-szego inequalitycoefficients estimatesrotation theorem |
| spellingShingle | Fatolah Hasanvand Shahram Najafzadeh Ali Ebadian New Subclass of Convex Functions Concerning Infinite Cone Sahand Communications in Mathematical Analysis univalent convexity subordination fekete-szego inequality coefficients estimates rotation theorem |
| title | New Subclass of Convex Functions Concerning Infinite Cone |
| title_full | New Subclass of Convex Functions Concerning Infinite Cone |
| title_fullStr | New Subclass of Convex Functions Concerning Infinite Cone |
| title_full_unstemmed | New Subclass of Convex Functions Concerning Infinite Cone |
| title_short | New Subclass of Convex Functions Concerning Infinite Cone |
| title_sort | new subclass of convex functions concerning infinite cone |
| topic | univalent convexity subordination fekete-szego inequality coefficients estimates rotation theorem |
| url | https://scma.maragheh.ac.ir/article_709283_84739b66a34d93ea1b4d5887d2ebc69b.pdf |
| work_keys_str_mv | AT fatolahhasanvand newsubclassofconvexfunctionsconcerninginfinitecone AT shahramnajafzadeh newsubclassofconvexfunctionsconcerninginfinitecone AT aliebadian newsubclassofconvexfunctionsconcerninginfinitecone |