{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:33Z","timestamp":1760150913918,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,4]],"date-time":"2022-02-04T00:00:00Z","timestamp":1643932800000},"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>The main purpose of this article is to introduce the new subclass of analytic functions whose coefficients are Borel distributions in the Janowski domain. Further, we investigate some useful number of properties such as Fekete\u2013Szeg\u0151 inequality, necessary and sufficient condition, growth and distortion approximations, convex linear combination, arithmetic mean, radii of close-to-convexity and starlikeness and partial sums, followed by some extremal functions for this defined class. The symmetry properties and other properties of the subclass of functions introduced in this paper can be studied as future research directions.<\/jats:p>","DOI":"10.3390\/sym14020322","type":"journal-article","created":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T20:40:18Z","timestamp":1644180018000},"page":"322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3716-2818","authenticated-orcid":false,"given":"Bakhtiar","family":"Ahmad","sequence":"first","affiliation":[{"name":"Government Degree College Mardan, Mardan 23200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2239-6416","authenticated-orcid":false,"given":"Muhammad Ghaffar","family":"Khan","sequence":"additional","affiliation":[{"name":"Institute of Numerical Sciences, Kohat University of Science and Technology Kohat, Kohat 26000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0269-0688","authenticated-orcid":false,"given":"Lumini\u0163a-Ioana","family":"Cot\u00eerl\u0103","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,4]]},"reference":[{"key":"ref_1","first-page":"5","article-title":"Poisson distribution series for certain subclasses of starlike functions with negative coefficients","volume":"24","author":"Altinkaya","year":"2017","journal-title":"Ann. 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