{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:07Z","timestamp":1760235907586,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,1]],"date-time":"2021-10-01T00:00:00Z","timestamp":1633046400000},"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>By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.<\/jats:p>","DOI":"10.3390\/sym13101840","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions"],"prefix":"10.3390","volume":"13","author":[{"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3716-2818","authenticated-orcid":false,"given":"Bakhtiar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Government Degree College Mardan, Mardan 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\/0000-0002-3950-6864","authenticated-orcid":false,"given":"Serkan","family":"Araci","sequence":"additional","affiliation":[{"name":"Department of Economics, Faculty of Economics Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep 27410, Turkey"}]},{"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":[[2021,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.na.2009.07.052","article-title":"On the Durrmeyer type modification of the q-Baskakov type operators","volume":"72","author":"Aral","year":"2010","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_2","first-page":"109","article-title":"On q-Baskakov type operators","volume":"42","author":"Aral","year":"2009","journal-title":"Demonstr. Math."},{"key":"ref_3","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. J. Pure Appl. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1017\/S0080456800002751","article-title":"On q-functions and a certain difference operator","volume":"46","author":"Jackson","year":"1909","journal-title":"Trans. R. Soc. Edinb."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"619","DOI":"10.2478\/s12175-011-0032-3","article-title":"Generalized q-Baskakov operators","volume":"61","author":"Aral","year":"2011","journal-title":"Math. Slovaca"},{"key":"ref_6","first-page":"249","article-title":"On the generalized Picard and Gauss Weierstrass singular integrals","volume":"8","author":"Aral","year":"2006","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"425","DOI":"10.4134\/JKMS.2006.43.2.425","article-title":"Geometric and approximation properties of generalized singular integrals","volume":"23","author":"Anastassiu","year":"2006","journal-title":"J. Korean Math. Soc."},{"key":"ref_8","first-page":"17231","article-title":"Geometric and approximation properties of some singular integrals in the unit disk","volume":"2006","author":"Anastassiu","year":"2006","journal-title":"J. Inequal. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"806168","DOI":"10.1155\/2014\/806168","article-title":"On a Subclass of Meromorphic Close-to-Convex Functions","volume":"2014","author":"Li","year":"2014","journal-title":"Sci. World J."},{"key":"ref_10","unstructured":"Srivastava, H.M., and Owa, S. (1989). Univalent functions, fractional calculus, and associated generalized hypergeometric functions. Univalent Functions, Fractional Calculus, and Their Applications, John Wiley and Sons."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.2478\/s12175-014-0268-9","article-title":"Some class of analytic functions related to conic domains","volume":"64","author":"Kanas","year":"2014","journal-title":"Math. Slovaca"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"958563","DOI":"10.1155\/2014\/958563","article-title":"Some subordination results on q-analogue of Ruscheweyh differential operator","volume":"2014","author":"Aldweby","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Srivastava, H.M., Khan, N., Khan, S., Ahmad, Q.Z., and Khan, B. (2021). A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator. Mathematics, 9.","DOI":"10.3390\/math9151812"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1515\/ms-2017-0166","article-title":"New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator","volume":"68","author":"Arif","year":"2018","journal-title":"Math. Slovaca"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.3934\/math.2021185","article-title":"On q-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain","volume":"6","author":"Ahmad","year":"2021","journal-title":"AIMS Math."},{"key":"ref_17","first-page":"75","article-title":"New subfamily of meromorphic convex functions in circular domain involving q-operator","volume":"16","author":"Ahmad","year":"2018","journal-title":"Int. J. Anal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Islam, S., Khan, M.G., Ahmad, B., Arif, M., and Chinram, R. (2020). Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function. Mathematics, 8.","DOI":"10.3390\/math8101676"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Shi, L., Khan, M.G., and Ahmad, B. (2020). Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator. Symmetry, 12.","DOI":"10.3390\/sym12020291"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1186\/s13660-019-2020-z","article-title":"A certain subclass of meromorphically q-starlike functions associated with the Janowski functions","volume":"2019","author":"Mahmood","year":"2019","journal-title":"J. Inequal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mahmood, S., Srivastava, H.M., Khan, N., Ahmad, Q.Z., Khan, B., and Ali, I. (2019). Upper bound of the third Hankel determinant for a subclass of q-starlike functions. Symmetry, 11.","DOI":"10.3390\/sym11030347"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.3934\/math.2021067","article-title":"Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions","volume":"6","author":"Rehman","year":"2021","journal-title":"AIMS Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.3934\/math.2021061","article-title":"Applications of a certain integral operator to the subclasses of analytic and bi-univalent functions","volume":"6","author":"Khan","year":"2021","journal-title":"AIMS Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102942","DOI":"10.1016\/j.bulsci.2020.102942","article-title":"Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function","volume":"167","author":"Srivastava","year":"2021","journal-title":"Bull. Sci. Math."},{"key":"ref_25","first-page":"5534357","article-title":"Applications of a New q-Difference Operator in Janowski-Type Meromorphic Convex Functions","volume":"2021","author":"Ahmad","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hu, Q., Srivastava, H., Ahmad, B., Khan, N., Khan, M., Mashwani, W., and Khan, B. (2021). A subclass of multivalent Janowski type q-Starlike functions and its consequences. Symmetry, 13.","DOI":"10.3390\/sym13071275"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1016\/S0252-9602(12)60106-4","article-title":"On certain class of meromorphic functions with positive coefcients","volume":"32","author":"Dziok","year":"2012","journal-title":"Acta Math. Sci. B"},{"key":"ref_28","first-page":"529","article-title":"Integral operator defined by q-analogue of Liu-Srivastava operator","volume":"58","author":"Huda","year":"2013","journal-title":"Stud. Univ. Babes-Bolyai Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"221","DOI":"10.2140\/pjm.1963.13.221","article-title":"On meromorphic starlike functions","volume":"13","author":"Pommerenke","year":"1963","journal-title":"Pac. J. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"135","DOI":"10.7153\/jmi-10-11","article-title":"Coefficient estimates of new classes of q-starlike and q-convex functions of complex order","volume":"10","author":"Seoudy","year":"2016","journal-title":"J. Math. Inequal."},{"key":"ref_31","first-page":"279","article-title":"Certain diferential operators for meromorphic functions","volume":"17","author":"Uralegaddi","year":"1991","journal-title":"Houst. J. Math."},{"key":"ref_32","first-page":"48","article-title":"On the coefficients of subordinate functions","volume":"48","author":"Rogosinski","year":"1943","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_33","first-page":"1501","article-title":"Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformatioons","volume":"22","author":"Srivastava","year":"2021","journal-title":"J. Nonlinear Convex Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1840\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:08:35Z","timestamp":1760166515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1840"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,1]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101840"],"URL":"https:\/\/doi.org\/10.3390\/sym13101840","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,1]]}}}