{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T22:22:43Z","timestamp":1785018163418,"version":"3.55.0"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,18]],"date-time":"2018-08-18T00:00:00Z","timestamp":1534550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym10080348","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T11:23:06Z","timestamp":1534764186000},"page":"348","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes"],"prefix":"10.3390","volume":"10","author":[{"given":"Nak Eun","family":"Cho","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Virendra","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ramanujan college, University of Delhi, H-Block, Kalkaji, New Delhi 110019, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Ravichandran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu 620015, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"159","DOI":"10.4064\/ap-23-2-159-177","article-title":"Extremal problems for a family of functions with positive real part and for some related families","volume":"23","author":"Janowski","year":"1970","journal-title":"Ann. 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