{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:03:39Z","timestamp":1765357419015,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T00:00:00Z","timestamp":1691020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli\u2019s numbers of the second kind. Let \u03c6BS(\u03be)=\u03bee\u03be\u221212=\u2211n=0\u221e\u03benBn2n!, where the coefficients of Bn2 are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions \ud835\udfca such that \u03be\ud835\udfca\u2032(\u03be)\ud835\udfca(\u03be)\u227a\u03c6BS(\u03be). We found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class.<\/jats:p>","DOI":"10.3390\/axioms12080764","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T11:23:03Z","timestamp":1691061783000},"page":"764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Starlike Functions Associated with Bernoulli\u2019s Numbers of Second Kind"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7466-7930","authenticated-orcid":false,"given":"Mohsan","family":"Raza","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan"}]},{"given":"Mehak","family":"Tariq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4429-9393","authenticated-orcid":false,"given":"Jong-Suk","family":"Ro","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"},{"name":"Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"}]},{"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":[[2023,8,3]]},"reference":[{"key":"ref_1","unstructured":"Coen, L.E.S. (1996). Sums of Powers and the Bernoulli Numbers. [Master\u2019s Thesis, Eastern Illinois University]."},{"key":"ref_2","first-page":"70","article-title":"Convexity of some particular functions","volume":"29","author":"Mocnu","year":"1984","journal-title":"Stud. Univ. 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