{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:59:36Z","timestamp":1760147976503,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T00:00:00Z","timestamp":1678924800000},"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>Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural formula, certain sharp radii results such as radius of starlikeness and convexity of order \u03b1. It also finds a radius for ratios of analytic functions associated with Euler numbers.<\/jats:p>","DOI":"10.3390\/sym15030737","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T04:10:48Z","timestamp":1679026248000},"page":"737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Starlike Functions Associated with Secant Hyperbolic Function"],"prefix":"10.3390","volume":"15","author":[{"given":"Khadija","family":"Bano","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7466-7930","authenticated-orcid":false,"given":"Mohsan","family":"Raza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6178-8538","authenticated-orcid":false,"given":"Qin","family":"Xin","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7855-508X","authenticated-orcid":false,"given":"Fairouz","family":"Tchier","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8940-0569","authenticated-orcid":false,"given":"Sarfraz Nawaz","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,16]]},"reference":[{"unstructured":"Li, Z., Ren, F., Yang, L., and Zhang, S. (1994). Proceeding of Conference on Complex Analysis, International Press.","key":"ref_1"},{"key":"ref_2","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. Pol. 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