{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T06:27:17Z","timestamp":1769840837404,"version":"3.49.0"},"reference-count":11,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2017R1C1B5076778"],"award-info":[{"award-number":["NRF-2017R1C1B5076778"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let    \u03a3    be the class of meromorphic functions f of the form     f  ( \u03b6 )  = \u03b6 +  \u2211  n = 0  \u221e   a n    \u03b6   \u2212 n       which are analytic in     \u0394 : = { \u03b6 \u2208 C : | \u03b6 | &gt; 1 }    . For     n \u2208  N 0  : = N \u222a  { 0 }     , the nth Faber polynomial      \u03a6 n   ( w )      of     f \u2208 \u03a3     is a monic polynomial of degree n that is generated by a function     \u03b6  f \u2032   ( \u03b6 )  \/  ( f  ( \u03b6 )  \u2212 w )     . For given     f \u2208 \u03a3    , by      F  n , i    ( f )     , we denote the ith coefficient of      \u03a6 n   ( w )     . For given     0 \u2264 \u03b1 &lt; 1     and     0 &lt; \u03b2 \u2264 1    , let us consider domains     H \u03b1     and      S \u03b2  \u2282 C     defined by      H \u03b1  =  { w \u2208 C : Re  ( w )  &gt; \u03b1 }      and      S \u03b2  =  { w \u2208 C : | arg  ( w )  | &lt; \u03b2 }     , which are symmetric with respect to the real axis. A function     f \u2208 \u03a3     is called meromorphic starlike of order    \u03b1    if     \u03b6  f \u2032   ( \u03b6 )  \/ f  ( \u03b6 )  \u2208  H \u03b1      for all     \u03b6 \u2208 \u0394    . Another function     f \u2208 \u03a3     is called meromorphic strongly starlike of order    \u03b2    if     \u03b6  f \u2032   ( \u03b6 )  \/ f  ( \u03b6 )  \u2208  S \u03b2      for all     \u03b6 \u2208 \u0394    . In this paper we investigate the sharp bounds of      F  n , n \u2212 i    ( f )     ,     n \u2208  N 0     ,     i \u2208 { 2 , 3 , 4 }    , for meromorphic starlike functions of order    \u03b1    and meromorphic strongly starlike of order    \u03b2   . Similar estimates for meromorphic convex functions of order    \u03b1    (    0 \u2264 \u03b1 &lt; 1    ) and meromorphic strongly convex of order    \u03b2    (    0 &lt; \u03b2 \u2264 1    ) are also discussed.<\/jats:p>","DOI":"10.3390\/sym11111368","type":"journal-article","created":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T10:49:07Z","timestamp":1572864547000},"page":"1368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions"],"prefix":"10.3390","volume":"11","author":[{"given":"Oh Sang","family":"Kwon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6741-9752","authenticated-orcid":false,"given":"Young Jae","family":"Sim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}]},{"given":"Saqib","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22060, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.2140\/pjm.1963.13.221","article-title":"On meromorphic starlike functions","volume":"13","author":"Pommerenke","year":"1963","journal-title":"Pac. 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Math."},{"key":"ref_6","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1090\/S0002-9939-1982-0652447-5","article-title":"Early coefficients of the inverse of a regular convex function","volume":"85","author":"Libera","year":"1982","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_8","first-page":"251","article-title":"Coefficient bounds for the inverse of a function with derivatives in P","volume":"87","author":"Libera","year":"1983","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s40315-017-0229-8","article-title":"On the fourth coefficient of functions in the Carath\u00e9odory class","volume":"18","author":"Kwon","year":"2018","journal-title":"Comp. Meth. Funct. Theory"},{"key":"ref_10","unstructured":"Goodman, A.W. (1983). Univalent Functions, Mariner Publishing Company."},{"key":"ref_11","unstructured":"Prokhorov, D.V., and Szynal, J. (2019, July 25). Inverse Coefficients for (\u03b1,\u03b2)-Convex Functions. Available online: https:\/\/www.researchgate.net\/publication\/265427362_Inverse_coefficients_for_a_b_-convex_functions."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1368\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:31:47Z","timestamp":1760189507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,4]]},"references-count":11,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["sym11111368"],"URL":"https:\/\/doi.org\/10.3390\/sym11111368","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,4]]}}}