Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes
Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are consider...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/8/348 |
| _version_ | 1811298006835658752 |
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| author | Nak Eun Cho Virendra Kumar V. Ravichandran |
| author_facet | Nak Eun Cho Virendra Kumar V. Ravichandran |
| author_sort | Nak Eun Cho |
| collection | DOAJ |
| description | Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction. |
| first_indexed | 2024-04-13T06:13:21Z |
| format | Article |
| id | doaj.art-641ef0e41a904413a2d1eeba825f25b6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:13:21Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-641ef0e41a904413a2d1eeba825f25b62022-12-22T02:58:56ZengMDPI AGSymmetry2073-89942018-08-0110834810.3390/sym10080348sym10080348Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski ClassesNak Eun Cho0Virendra Kumar1V. Ravichandran2Department of Applied Mathematics, Pukyong National University, Busan 48513, KoreaDepartment of Mathematics, Ramanujan college, University of Delhi, H-Block, Kalkaji, New Delhi 110019, IndiaDepartment of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu 620015, IndiaHigher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction.http://www.mdpi.com/2073-8994/10/8/348higher order Schwarzian derivativesJanowski star-like functionJanowski convex functionbound on derivatives |
| spellingShingle | Nak Eun Cho Virendra Kumar V. Ravichandran Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes Symmetry higher order Schwarzian derivatives Janowski star-like function Janowski convex function bound on derivatives |
| title | Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes |
| title_full | Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes |
| title_fullStr | Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes |
| title_full_unstemmed | Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes |
| title_short | Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes |
| title_sort | sharp bounds on the higher order schwarzian derivatives for janowski classes |
| topic | higher order Schwarzian derivatives Janowski star-like function Janowski convex function bound on derivatives |
| url | http://www.mdpi.com/2073-8994/10/8/348 |
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