{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T16:59:41Z","timestamp":1778000381773,"version":"3.51.4"},"reference-count":47,"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\/"}],"funder":[{"name":"University of Oradea"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided.<\/jats:p>","DOI":"10.3390\/sym15030713","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T06:09:56Z","timestamp":1678687796000},"page":"713","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Strong Differential Subordination and Superordination Results for Extended q-Analogue of Multiplier Transformation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7535","authenticated-orcid":false,"given":"Alina Alb","family":"Lupa\u015f","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8586-2539","authenticated-orcid":false,"given":"Firas","family":"Ghanim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2307\/2370183","article-title":"q-Difference equations","volume":"32","author":"Jackson","year":"1910","journal-title":"Am. J. Math."},{"key":"ref_2","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Quart. J. Pure Appl. Math."},{"key":"ref_3","first-page":"77","article-title":"A generalization of starlike functions","volume":"14","author":"Ismail","year":"1990","journal-title":"Complex Var. Theory Appl."},{"key":"ref_4","unstructured":"Srivastava, H.M., and Owa, S. (1989). Univalent Functions, Fractional Calculus, and Their Applications, John Wiley and Sons."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"020001","DOI":"10.1063\/1.5097511","article-title":"Use of Quantum Calculus approach in Mathematical Sciences and its role in geometric function theory","volume":"2095","author":"Ahuja","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"ref_6","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_7","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_8","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10476-017-0206-5","article-title":"On a class of analytic functions related to conic domains involving q-calculus","volume":"43","author":"Govindaraj","year":"2017","journal-title":"Anal. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Khan, B., Srivastava, H.M., Arjika, S., Khan, S., Khan, N., and Ahmad, Q.Z. (2021). A certain q-Ruscheweyh type derivative operator and its applications involving multivalent functions. Adv. Differ. Equ., 279.","DOI":"10.1186\/s13662-021-03441-6"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s11139-020-00338-y","article-title":"Coefficient estimates for a certain family of analytic functions involving a q-derivative operator","volume":"55","author":"Raza","year":"2021","journal-title":"Ramanujan J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Amini, E., Fardi, M., Al-Omari, S., and Nonlaopon, K. (2022). Results on Univalent Functions Defined by q-Analogues of S\u0103l\u0103gean and Ruscheweh Operators. Symmetry, 14.","DOI":"10.3390\/sym14081725"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Alb Lupa\u015f, A. (2022). Subordination Results on the q-Analogue of the S\u0103l\u0103gean Differential Operator. Symmetry, 14.","DOI":"10.3390\/sym14081744"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hadid, S.B., Ibrahim, R.W., and Momani, S. (2022). Multivalent Functions and Differential Operator Extended by the Quantum Calculus. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6070354"},{"key":"ref_14","first-page":"3","article-title":"On q-Bernardi integral operator","volume":"8","author":"Noor","year":"2017","journal-title":"TWMS J. Pure Appl. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2707","DOI":"10.3906\/mat-1907-41","article-title":"Study on q-analogue of certain family of linear operators","volume":"43","author":"Shah","year":"2019","journal-title":"Turkish J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1006\/jdeq.1994.1142","article-title":"Strong differential subordination to Briot-Bouquet differential equations","volume":"114","author":"Antonino","year":"1994","journal-title":"J. Differ. Equ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0022-247X(78)90181-6","article-title":"Second order-differential inequalities in the complex plane","volume":"65","author":"Miller","year":"1978","journal-title":"J. Math. Anal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1307\/mmj\/1029002507","article-title":"Differential subordinations and univalent functions","volume":"28","author":"Miller","year":"1981","journal-title":"Mich. Math. J."},{"key":"ref_19","first-page":"249","article-title":"Strong differential subordination","volume":"33","author":"Oros","year":"2009","journal-title":"Turk. J. Math."},{"key":"ref_20","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Theory and Applications, Marcel Dekker, Inc."},{"key":"ref_21","first-page":"101","article-title":"Strong differential superordination","volume":"19","author":"Oros","year":"2009","journal-title":"Acta Univ. Apulensis"},{"key":"ref_22","first-page":"815","article-title":"Subordinations of differential superordinations","volume":"48","author":"Miller","year":"2003","journal-title":"Complex Var."},{"key":"ref_23","first-page":"293","article-title":"Best Subordinants of the Strong Differential Superordination","volume":"38","author":"Oros","year":"2009","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1016\/j.jmaa.2011.07.016","article-title":"Strong differential subordination and superordination of analytic functions","volume":"385","author":"Jeyaraman","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"ref_25","first-page":"221","article-title":"Some strong differential subordinations obtained by S\u0103l\u0103gean differential operator","volume":"55","year":"2010","journal-title":"Stud. Univ. Babe\u015f-Bolyai Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1080\/10652460903494751","article-title":"Strong differential subordination and superordination for multivalently meromorphic functions involving the Liu\u2013Srivastava operator","volume":"21","author":"Cho","year":"2010","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_27","first-page":"328","article-title":"Strong differential subordinations obtained by Ruscheweyh operator","volume":"14","year":"2012","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_28","first-page":"27","article-title":"Certain strong differential subordinations using S\u0103l\u0103gean and Ruscheweyh operators","volume":"6","year":"2011","journal-title":"Adv. Appl. Math. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1016\/j.aml.2011.09.074","article-title":"On special strong differential subordinations using multiplier transformation","volume":"25","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_30","first-page":"285","article-title":"Some strong differential subordinations using a new generalized multiplier transformation","volume":"34","author":"Swamy","year":"2013","journal-title":"Acta Univ. Apulensis"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1186\/1687-2770-2013-44","article-title":"Strong differential subordination properties for analytic functions involving the Komatu integral operator","volume":"2013","author":"Cho","year":"2013","journal-title":"Bound. Value Probl."},{"key":"ref_32","first-page":"26","article-title":"Strong differential subordination and superordination of analytic functions associated with Komatu operator","volume":"4","author":"Jeyaramana","year":"2013","journal-title":"Int. J. Nonlinear Anal. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"20210839","DOI":"10.1098\/rspa.2021.0839","article-title":"Certain implementations in fractional calculus operators involving Mittag-Leffler-confluent hypergeometric functions","volume":"478","author":"Ghanim","year":"2022","journal-title":"Proc. R. Soc. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1080\/25765299.2021.1930637","article-title":"Some analytical merits of Kummer-type function associated with Mittag-Leffler parameters","volume":"28","author":"Ghanim","year":"2021","journal-title":"Arab. J. Basic Appl. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ghanim, F., Al-Janaby, H.F., and Bazighifan, O. (2021). Some New Extensions on Fractional Differential and Integral Properties for Mittag-Leffler Confluent Hypergeometric Function. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5040143"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"143","DOI":"10.37193\/CJM.2015.02.01","article-title":"Some strong differential subordinations using a differential operator","volume":"31","author":"Andrei","year":"2015","journal-title":"Carpathian J. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"503","DOI":"10.11568\/kjm.2015.23.4.503","article-title":"Strong differential subordination and superordination of new generalized derivative operator","volume":"23","author":"Oshah","year":"2015","journal-title":"Korean J. Math."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"45","DOI":"10.5937\/MatMor1902045S","article-title":"Strong Differential Sandwich Results of \u03bb-Pseudo-Starlike Functions with Respect to Symmetrical Points","volume":"23","author":"Srivastava","year":"2019","journal-title":"Math. Morav."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"27","DOI":"10.46793\/KgJMat2001.027W","article-title":"New strong differential subordination and superordination of meromorphic multivalent quasi-convex functions","volume":"44","author":"Wanas","year":"2020","journal-title":"Kragujev. J. Math."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"012113","DOI":"10.1088\/1742-6596\/1818\/1\/012113","article-title":"Strong subordination for p-valent functions involving a linear operator","volume":"1818","author":"Abd","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_41","first-page":"445","article-title":"On a first order strong differential subordination and application to univalent functions","volume":"37","author":"Aghalary","year":"2022","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_42","first-page":"5495011","article-title":"A Study of Spiral-Like Harmonic Functions Associated with Quantum Calculus","volume":"2022","author":"Shah","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"6642","DOI":"10.3934\/math.2023336","article-title":"On fuzzy differential subordination associated with q-difference operator","volume":"8","author":"Shah","year":"2023","journal-title":"AIMS Math."},{"key":"ref_44","first-page":"243","article-title":"On a new strong differential subordination","volume":"32","author":"Oros","year":"2012","journal-title":"Acta Univ. Apulensis"},{"key":"ref_45","first-page":"1","article-title":"On special strong differential superordinations using S\u0103l\u0103gean and Ruscheweyh operators","volume":"1","year":"2014","journal-title":"J. Adv. Appl. Comput. Math."},{"key":"ref_46","first-page":"266","article-title":"On special strong differential subordinations using S\u0103l\u0103gean and Ruscheweyh operators","volume":"14","author":"Oros","year":"2012","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Alb Lupa\u015f, A., and Oros, G.I. (2021). Strong differential superordination results involving extended Salagean and Ruscheweyh operators. 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