{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:51:21Z","timestamp":1760230281677,"version":"build-2065373602"},"reference-count":34,"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\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and the modified sigmoid function. The results contained in the proved theorems refer to coefficient estimates for the functions in the newly introduced classes.<\/jats:p>","DOI":"10.3390\/sym14071479","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T08:28:25Z","timestamp":1658219305000},"page":"1479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function"],"prefix":"10.3390","volume":"14","author":[{"given":"Jamiu Olusegun","family":"Hamzat","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Lagos, Lagos 101017, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6472-2430","authenticated-orcid":false,"given":"Abiodun Tinuoye","family":"Oladipo","sequence":"additional","affiliation":[{"name":"Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 210214, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,19]]},"reference":[{"key":"ref_1","first-page":"313","article-title":"Modified sigmoid function in univalent function theory","volume":"7","author":"Oladipo","year":"2013","journal-title":"Int. J. Math. Sci. Engr. Appl."},{"key":"ref_2","first-page":"392","article-title":"Coefficient Bounds for Bazilevic Functions Involving Logistic Sigmoid Function Associated with Conic Domains","volume":"2018","author":"Hamzat","year":"2018","journal-title":"Int. J. Math. Anal. Opt. Theory Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.12732\/ijpam.v101i1.4","article-title":"Sigmoid function in the space of univalent \u03bb-Pseudo starlike functions","volume":"101","author":"Murugusundaramorthy","year":"2015","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_4","first-page":"61","article-title":"Subordination results for Logistic Sigmoid Function in the Space of Univalent functions in the unit disk","volume":"12","author":"Oladipo","year":"2014","journal-title":"Adv. Comput. Sci. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1016\/j.aml.2010.05.009","article-title":"Certain subclasses of analytic and bi-univalent functions","volume":"23","author":"Srivastava","year":"2010","journal-title":"Appl. Math. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pall-Szabo, A.O., and Oros, G.I. (2020). Coefficient related studies for new classes of bi-univalent functions. Mathematics, 8.","DOI":"10.3390\/math8071110"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.2298\/FIL1307165C","article-title":"Coefficient bounds for new subclasses of bi-univalent functions","volume":"27","author":"Caglar","year":"2013","journal-title":"Filomat"},{"key":"ref_8","first-page":"49","article-title":"Certain subclasses of bi-univalent functions satisfying subordination conditions","volume":"2","author":"Deniz","year":"2013","journal-title":"J. Class. Annal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/s13370-016-0478-0","article-title":"Coefficient estimates for some general subclasses of analytic and bi-univalent functions","volume":"28","author":"Srivastava","year":"2017","journal-title":"Afr. Mat."},{"key":"ref_10","first-page":"493","article-title":"Initial Maclaurin coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination","volume":"59","author":"Srivastava","year":"2019","journal-title":"Kyungpook Math. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.3906\/mat-1511-41","article-title":"Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions","volume":"40","author":"Bulut","year":"2016","journal-title":"Turk. J. Math."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Breaz, D., and Cotirla, L.I. (2022). The study of the new classes of m-fold symmetric bi-univalent functions. Mathematics, 10.","DOI":"10.3390\/math10010075"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hamidi, S.G., and Jahangiri, J.M. (2014). Unpredictability of the coefficients of m-fold symmetric bi-starlike functions. Int. J. Math., 25.","DOI":"10.1142\/S0129167X14500645"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107","DOI":"10.32513\/tmj\/1932200819","article-title":"Some properties of a new subclass of m-Fold Symmetric bi-Bazilevic functions associated with modified sigmoid Functions","volume":"14","author":"Hamzat","year":"2021","journal-title":"Tbilisi Math. J."},{"key":"ref_15","first-page":"807","article-title":"Coefficient Bounds For Certain New Subclass of m-Fold Symmetric Bi-Univalent Functions Associated with Conic Domains","volume":"3","author":"Hamzat","year":"2018","journal-title":"Trends Sci. Tech. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Oros, G.I., and Cotirla, L.I. (2022). Coefficient estimates and the Fekete-Szego problem for new classes of m-fold symmetric bi-univalent functions. Mathematics, 10.","DOI":"10.3390\/math10010129"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"831","DOI":"10.2298\/FIL1305831S","article-title":"Coefficient estimates for a general subclass of analytic and bi-univalent functions","volume":"27","author":"Srivastava","year":"2013","journal-title":"Filomat"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.7153\/jca-02-14","article-title":"Coefficient estimates for some families of Bi-Bazilevic functions of the Ma-Minda type involving the Hohlov operator","volume":"2","author":"Srivastava","year":"2013","journal-title":"J. Class. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Atshan, W.G., Rahman, I.A.R., and Alb Lupa\u015f, A. (2021). Some Results of New Subclasses for Bi-Univalent Functions Using Quasi-Subordination. Symmetry, 13.","DOI":"10.3390\/sym13091653"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Alb Lupa\u015f, A., and El-Deeb, S.M. (2022). Subclasses of Bi-Univalent Functions Connected with Integral Operator Based upon Lucas Polynomial. Symmetry, 14.","DOI":"10.3390\/sym14030622"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"659","DOI":"10.24193\/subbmath.2021.4.05","article-title":"Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions","volume":"66","author":"Wanas","year":"2021","journal-title":"Stud. Univ. Babes-Bolyai Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"289","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_23","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_24","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations. Theory and Applications, Marcel Dekker, Inc.","DOI":"10.1201\/9781482289817"},{"key":"ref_25","first-page":"1751","article-title":"Inclusion Properties of Certain Subclasses of Analytic Functions","volume":"7","author":"Swamy","year":"2012","journal-title":"Inter. Math. Forum"},{"key":"ref_26","unstructured":"Hamzat, J.O., and El-Ashwah, R.M. (2021). Some properties of a generalized multiplier transform on analytic p-valent functions. Ukr. J. Math., accepted."},{"key":"ref_27","first-page":"24","article-title":"A generalized multiplier transform on a univalent integral operator","volume":"9","author":"Makinde","year":"2019","journal-title":"J. Contemp. Appl. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S0895-7177(03)80004-3","article-title":"Argument estimates of certain analytic functions defined by a class of multiplier transformations","volume":"37","author":"Cho","year":"2003","journal-title":"Math. Comput. Model."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"399","DOI":"10.4134\/BKMS.2003.40.3.399","article-title":"Multiplier transformations and strongly Close-to-Convex functions","volume":"40","author":"Cho","year":"2003","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_30","unstructured":"Duren, P.L. (1983). Univalent Functions, Springer."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1090\/S0002-9939-1967-0206255-1","article-title":"On a coefficient problem for bi-univalent functions","volume":"18","author":"Lewin","year":"1967","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_32","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_33","first-page":"75","article-title":"On the upper bound of the third Hankel determinant for certain class of analytic functions related with exponential functions","volume":"30","author":"Breaz","year":"2022","journal-title":"An. St. Univ. Ovidius Constanta"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Rahman, I.A.R., Atshan, W.G., and Oros, G.I. (2022). New concept on fourth Hankel determinant of a cetrtain subclass of analytic functions. Afr. Mat., 33.","DOI":"10.1007\/s13370-021-00957-8"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1479\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:53:52Z","timestamp":1760140432000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1479"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,19]]},"references-count":34,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071479"],"URL":"https:\/\/doi.org\/10.3390\/sym14071479","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,7,19]]}}}