{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:24:32Z","timestamp":1769552672137,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T00:00:00Z","timestamp":1658188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Institutional Fund Projects from the Ministry of Education and Deanship of Scientific Research (DSR)","award":["IFPDP-206-22"],"award-info":[{"award-number":["IFPDP-206-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes some known results, as well as provides some new ones.<\/jats:p>","DOI":"10.3390\/sym14071471","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T05:37:53Z","timestamp":1658209073000},"page":"1471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0694-4358","authenticated-orcid":false,"given":"Abdel Moneim Y.","family":"Lashin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7498-2228","authenticated-orcid":false,"given":"Abeer O.","family":"Badghaish","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8840-420X","authenticated-orcid":false,"given":"Badriah Maeed","family":"Algethami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,19]]},"reference":[{"key":"ref_1","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":"1908","journal-title":"Trans. R. Soc. Edinb."},{"key":"ref_2","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. J. Pure Appl. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1016\/j.camwa.2012.01.076","article-title":"The q-symmetric variational calculus","volume":"64","author":"Martins","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0034-4877(09)90021-0","article-title":"Basic-deformed quantum mechanics","volume":"64","author":"Lavagno","year":"2009","journal-title":"Rep. Math. Phys."},{"key":"ref_5","unstructured":"Lupas, A. (1987). A q-analogue of the Bernstein operator. Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca. Preprint, pp. 87\u201389; MR0956939 (90b:41026)."},{"key":"ref_6","first-page":"77","article-title":"A generalization of starlike functions","volume":"14","author":"Ismail","year":"1990","journal-title":"Complex Var. Theory Appl."},{"key":"ref_7","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"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s42787-022-00141-2","article-title":"Convolution conditions for two subclasses of analytic functions defined by Jackson q-difference operator","volume":"30","year":"2022","journal-title":"J. Egypt. Math. Soc."},{"key":"ref_9","first-page":"348","article-title":"New subclasses of analytic function associated with q-difference operator","volume":"10","author":"Frasin","year":"2017","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s10476-021-0092-8","article-title":"Nevanlinna theory for Jackson difference operators and entire solutions of q-difference equations","volume":"47","author":"Cao","year":"2021","journal-title":"Anal. Math."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hasan, A.M., Jalab, H.A., Ibrahim, R.W., Meziane, F., Al-Shamasneh, A.R., and Obaiys, S.J. (2020). MRI brain classification using the quantum entropy LBP and deep-learning-based features. Entropy, 22.","DOI":"10.3390\/e22091033"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"622","DOI":"10.3934\/Math.2017.4.622","article-title":"Certain subclass of analytic functions related with conic domains and associated with Salagean q-differential operator","volume":"2","author":"Hussain","year":"2017","journal-title":"AIMS Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13398-020-00982-5","article-title":"On quantum hybrid fractional conformable differential and integral operators in a complex domain","volume":"115","author":"Ibrahim","year":"2021","journal-title":"Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A Mat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1186\/s13662-020-02788-6","article-title":"On subclasses of analytic functions based on a quantum symmetric conformable differential operator with the application","volume":"2020","author":"Ibrahim","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_15","first-page":"264","article-title":"Certain class of analytic functions involving Salagean type q-difference operator","volume":"6","author":"Kaliappan","year":"2018","journal-title":"Konuralp J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Annaby, M.H., and Mansour, Z.S. (2012). q-Fractional Calculus and Equations, Springer.","DOI":"10.1007\/978-3-642-30898-7"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gasper, G., and Rahman, M. (2004). Basic Hypergeometric Series, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511526251"},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1090\/S0002-9939-1975-0367176-1","article-title":"New criteria for univalent functions","volume":"49","author":"Ruscheweyh","year":"1975","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1090\/S0002-9939-1979-0545592-6","article-title":"Integrals of certain univalent functions","volume":"77","author":"Singh","year":"1979","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S179355712050134X","article-title":"Some properties for certain subclasses of analytic functions defined by a general differential operator","volume":"13","author":"Deniz","year":"2020","journal-title":"Asian-Eur. J. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"415319","DOI":"10.1155\/2013\/415319","article-title":"Coefficient estimates and other properties for a class of spirallike functions associated with a differential operator","volume":"2013","author":"Orhan","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"ref_23","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_24","first-page":"8459405","article-title":"On Fekete\u2013Szeg\u00f6 problems for certain subclasses of analytic functions defined by differential operator involving q-Ruscheweyh operator","volume":"2020","author":"Alsoboh","year":"2020","journal-title":"J. Funct. Spaces"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1007\/s13398-018-0539-3","article-title":"Some applications of a q-analogue of the Ruscheweyh type operator for multivalent functions","volume":"113","author":"Arif","year":"2019","journal-title":"Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A Mat."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Badar, R.S., and Noor, K.I. (2019). On q-uniformly Mocanu functions. Fractal Fract., 3.","DOI":"10.3390\/fractalfract3010005"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Noor, K.I. (2019). On analytic functions involving the q-Ruscheweyeh derivative. Fractal Fract., 3.","DOI":"10.3390\/fractalfract3010010"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10466","DOI":"10.3934\/math.2021607","article-title":"New subclass of analytic functions defined by q-analogue of p-valent Noor integral operator","volume":"6","author":"Aldawish","year":"2021","journal-title":"AIMS Math."},{"key":"ref_29","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_30","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1007\/s11253-019-01602-1","article-title":"Subclass of k-uniformly starlike functions defined by the symmetric q-derivative operator","volume":"70","author":"Kanas","year":"2019","journal-title":"Ukr. Math. J."},{"key":"ref_31","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_32","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1515\/dema-2021-0008","article-title":"On q-analogue of Janowski-type starlike functions with respect to symmetric points","volume":"54","author":"Khan","year":"2021","journal-title":"Demonstr. Math."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Khan, M.F. (2022). Properties of q-Starlike Functions Associated with the q-Cosine Function. Symmetry, 14.","DOI":"10.3390\/sym14061117"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s40590-019-00258-y","article-title":"On convolution and q-calculus","volume":"26","author":"Piejko","year":"2020","journal-title":"Bol. Soc. Mat. Mex."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2879","DOI":"10.1007\/s40995-019-00758-6","article-title":"On q-Calculus and Starlike Functions","volume":"43","author":"Piejko","year":"2019","journal-title":"Iran. J. Sci. Technol. Trans. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5869","DOI":"10.3934\/math.2021347","article-title":"Convolution properties of meromorphically harmonic functions defined by a generalized convolution q-derivative operator","volume":"6","author":"Srivastava","year":"2021","journal-title":"AIMS Math."},{"key":"ref_37","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_38","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_39","doi-asserted-by":"crossref","unstructured":"Zhao, W., Rexma Sherine, V., Gerly, T.G., Britto Antony Xavier, G., Julietraja, K., and Chellamani, P. (2022). Symmetric Difference Operator in Quantum Calculus. Symmetry, 14.","DOI":"10.3390\/sym14071317"},{"key":"ref_40","first-page":"283","article-title":"q-Harmonic mappings for which analytic part is q-convex functions","volume":"4","author":"Ademogullari","year":"2016","journal-title":"Nonlinear Anal. Differ. Equ."},{"key":"ref_41","first-page":"77","article-title":"Subclasses of univalent functions","volume":"11","author":"Goel","year":"1980","journal-title":"Tamkang J. Math."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1090\/S0002-9947-1969-0232920-2","article-title":"Convex and starlike univalent Functions","volume":"13","author":"Bernardi","year":"1969","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1090\/S0002-9939-1965-0178131-2","article-title":"Some classes of regular univalent functions","volume":"16","author":"Libera","year":"1965","journal-title":"Proc. Am. Math. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1471\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:53:33Z","timestamp":1760140413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,19]]},"references-count":43,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071471"],"URL":"https:\/\/doi.org\/10.3390\/sym14071471","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,19]]}}}