{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T14:31:04Z","timestamp":1780497064990,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T00:00:00Z","timestamp":1666137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"DAAD"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients. Using criteria due to Fej\u00e9r and Ozaki, we provide sufficient conditions for these functions to be close-to-convex or starlike inside the unit disk, and thus univalent. One of our proofs is assisted by symbolic computation.<\/jats:p>","DOI":"10.3390\/axioms11100568","type":"journal-article","created":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T20:32:23Z","timestamp":1666211543000},"page":"568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk"],"prefix":"10.3390","volume":"11","author":[{"given":"\u017divorad","family":"Tomovski","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ostrava, 701 03 Ostrava, Czech Republic"},{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Ss. Cyril and Methodius University, 1000 Skopje, North Macedonia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Gerhold","sequence":"additional","affiliation":[{"name":"Institute of Statistics and Mathematical Methods in Economics, Technische Universit\u00e4t Wien, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Deepak","family":"Bansal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College of Engineering and Technology, Bikaner 334004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2748-5776","authenticated-orcid":false,"given":"Amit","family":"Soni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government Engineering College, Bikaner 334004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,19]]},"reference":[{"key":"ref_1","unstructured":"Duren, P.L. 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