{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T11:25:54Z","timestamp":1771845954026,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571299"],"award-info":[{"award-number":["11571299"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Using differential subordination, we consider conditions of \u03b2 so that some multivalent analytic functions are subordinate to (1+z)\u03b3 (0&lt;\u03b3\u22641). Notably, these results are applied to derive sufficient conditions for f\u2208A to satisfy the condition zf\u2032(z)f(z)2\u22121&lt;1. Several previous results are extended.<\/jats:p>","DOI":"10.3390\/axioms10030160","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T09:25:52Z","timestamp":1627291552000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli"],"prefix":"10.3390","volume":"10","author":[{"given":"Likai","family":"Liu","sequence":"first","affiliation":[{"name":"Information Technology Department, Nanjing Vocational College of Information Technology, Nanjing 210023, China"}]},{"given":"Jin-Lin","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Information Science, Yangzhou University, Yangzhou 225002, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"ref_1","first-page":"101","article-title":"Radius of convexity of some subclasses of strongly starlike functions","volume":"19","author":"Stankiewicz","year":"1996","journal-title":"Zesz. 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J. Sci. Technol. Trans. A Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s11785-017-0690-4","article-title":"Subrodinations for functions with positive real part","volume":"12","author":"Kumar","year":"2018","journal-title":"Complex Anal. Oper. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"487","DOI":"10.24193\/subbmath.2019.4.04","article-title":"Differential superordination for harmonic complex-valued functions","volume":"64","author":"Oros","year":"2019","journal-title":"Stud. Univ. Babes-Bolyai Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s40995-019-00815-0","article-title":"Operators of basic (or q-) calculus and fractional q-calculus and their applications in Geometric Function Theory of complex analysis","volume":"44","author":"Srivastava","year":"2020","journal-title":"Iran. J. Sci. Technol. Trans. A Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"951","DOI":"10.18576\/amis\/110401","article-title":"Certain subordination-preserving family of integral operators associated with p-valent functions","volume":"11","author":"Srivastava","year":"2017","journal-title":"Appl. Math. Inform. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.2298\/FIL1909613S","article-title":"Some general families of q-starlike functions associated with the Janowski functions","volume":"33","author":"Srivastava","year":"2019","journal-title":"Filomat"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Srivastava, H.M., Tahir, M., Khan, B., Ahmad, Q.Z., and Khan, N. (2019). Some general classes of q-starlike functions associated with the Janowski functions. Symmetry, 11.","DOI":"10.3390\/sym11020292"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2298\/FIL1601113S","article-title":"A certain subclass of multivalent functions involving higher-order derivatives","volume":"30","author":"Srivastava","year":"2016","journal-title":"Filomat"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"407","DOI":"10.14492\/hokmj\/1562810517","article-title":"Coefficient inequalities for q-starlike functions associated with the Janowski functions","volume":"48","author":"Srivastava","year":"2019","journal-title":"Hokkaido Math. J."},{"key":"ref_14","first-page":"1782916","article-title":"On Subordinations for Certain Multivalent Analytic Functions in the Right-Half Plane","volume":"2016","author":"Xu","year":"2016","journal-title":"J. Funct. Spaces"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"943","DOI":"10.7153\/jmi-2018-12-71","article-title":"A family of meromorphic functions involving generalized Mittag-Leffler function","volume":"12","author":"Yan","year":"2018","journal-title":"J. Math. Inequal."},{"key":"ref_16","first-page":"6622230","article-title":"On certain class of Bazilevi\u010d functions associated with the Lemniscate of Bernoulli","volume":"2020","author":"Seoudy","year":"2020","journal-title":"J. Funct. Spaces"},{"key":"ref_17","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordination. 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