{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:09:53Z","timestamp":1760234993470,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T00:00:00Z","timestamp":1626393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Scientific Research Project of the Colleges and Universities in the Henan Province of the People\u2019s Republic of China","award":["Grant No.: 19A110024,  and  212300410204"],"award-info":[{"award-number":["Grant No.: 19A110024,  and  212300410204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class Ap, where class Ap is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p,q)-variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary.<\/jats:p>","DOI":"10.3390\/sym13071275","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"1275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences"],"prefix":"10.3390","volume":"13","author":[{"given":"Qiuxia","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Luoyang Normal University, Luoyang 471934, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3716-2818","authenticated-orcid":false,"given":"Bakhtiar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government Degree College Mardan, Marden 23200, Pakistan"}]},{"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, 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 26000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5081-741X","authenticated-orcid":false,"given":"Wali Khan","family":"Mashwani","sequence":"additional","affiliation":[{"name":"Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2427-2003","authenticated-orcid":false,"given":"Bilal","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,16]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Quart. 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