{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:58:22Z","timestamp":1760147902302,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T00:00:00Z","timestamp":1678665600000},"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>In the present paper, we develop some implications leading to Carath\u00e9odory functions in the open disk and provide some new conditions for functions to be p-valent functions. This work also extends the findings of Nunokawa and others.<\/jats:p>","DOI":"10.3390\/axioms12030295","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T06:09:56Z","timestamp":1678687796000},"page":"295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Sufficient Conditions on p-Valency for Certain Analytic Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3079-9944","authenticated-orcid":false,"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1484-7643","authenticated-orcid":false,"given":"Muhammad","family":"Arif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali khan University Mardan, Mardan 23200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5243-4252","authenticated-orcid":false,"given":"Syed Zakar Hussain","family":"Bukhari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mirpur University of Science and Technology, Mirpur 10250, Pakistan"}]},{"given":"Malik Ali","family":"Raza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mirpur University of Science and Technology, Mirpur 10250, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"key":"ref_1","unstructured":"Hayman, W.K. 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