{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:05:02Z","timestamp":1760151902351,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T00:00:00Z","timestamp":1669766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Taif University, Taif, Saudi Arabia","award":["TURSP-2020\/207"],"award-info":[{"award-number":["TURSP-2020\/207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In our present work, the concepts of symmetrical functions and the concept of spirallike Janowski functions are combined to define a new class of analytic functions. We give a structural formula for functions in S\u03b7,\u03bc(F,H,\u03bb), a representation theorem, the radius of starlikeness estimates, covering and distortion theorems and integral mean inequalities are obtained.<\/jats:p>","DOI":"10.3390\/sym14122526","type":"journal-article","created":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T04:05:24Z","timestamp":1669781124000},"page":"2526","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Some Properties of Janowski Symmetrical Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4759-5449","authenticated-orcid":false,"given":"Fuad","family":"Alsarari","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sciences College, Taibah University, P.O. Box 46421, Yanbu 41911, Saudi Arabia"}]},{"given":"Aljazi","family":"Alkhammash","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]},{"given":"Erhan","family":"Deniz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars 36100, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,30]]},"reference":[{"key":"ref_1","unstructured":"Nehari, Z. (1952). Conformal Mapping, McGraw-Hill."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.4064\/ap-28-3-297-326","article-title":"Some extremal problems for certain families of analytic functions","volume":"28","author":"Janowski","year":"1973","journal-title":"Ann. Pol. Math."},{"key":"ref_3","first-page":"12","article-title":"Prispevek k teorii funkei prostych","volume":"62","year":"1933","journal-title":"Cas. 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Math."},{"key":"ref_8","first-page":"255","article-title":"Growth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc","volume":"57","author":"Polatoglu","year":"2012","journal-title":"Stud. Univ. Babes-Bolyai Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"143","DOI":"10.4134\/CKMS.2013.28.1.143","article-title":"A certain subclass of Janowski type functions associated with ksymmetic points","volume":"28","author":"Kwon","year":"2013","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_10","first-page":"556","article-title":"A few results on functions that are Janowski starlike related to (j,k)-symmetric points","volume":"21","author":"Alsarari","year":"2013","journal-title":"Octag. Math. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"72","DOI":"10.2969\/jmsj\/01110072","article-title":"On a certain univalent mapping","volume":"11","author":"Sakaguchi","year":"1959","journal-title":"J. Math. Soc. Jpn."},{"key":"ref_12","first-page":"389","article-title":"A few results on Janowski functions associated with k-symmetric points","volume":"25","author":"Alsarari","year":"2017","journal-title":"Korean J. Math."},{"key":"ref_13","first-page":"53","article-title":"Some remarks on functions starlike with respect to symmetric points","volume":"19","author":"Stankiewicz","year":"1965","journal-title":"Ann. Univ. Mariae-Curie Skledowke"},{"key":"ref_14","first-page":"61","article-title":"On the class of univalent functions starlike with respect to N-symmetric points","volume":"31","author":"Nezhmetdinov","year":"2002","journal-title":"Hokkaido Math. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1090\/S0002-9939-1957-0086879-9","article-title":"Univalent functions and nonanalytic curves","volume":"8","author":"Goodman","year":"1975","journal-title":"Proc. Am. Math. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2526\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:29:56Z","timestamp":1760146196000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,30]]},"references-count":15,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["sym14122526"],"URL":"https:\/\/doi.org\/10.3390\/sym14122526","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,11,30]]}}}