{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:56Z","timestamp":1760057876297,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T00:00:00Z","timestamp":1741132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]},{"name":"Natural Science Foundation of China","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]},{"name":"Natural Science Foundation of Inner Mongolia of China","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]},{"name":"program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]},{"name":"program for Key Laboratory Construction of Chifeng University","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]},{"name":"Research and Innovation Team of Complex Analysis and Nonlinear Dynamic Systems of Chifeng University","award":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"],"award-info":[{"award-number":["KFU250784","11561001","11761006","12261003","2022MS01004","2021MS01002","NJYT-18-A14","CFXYZD202004","cfxykycxtd202005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, a new subclass of starlike functions is defined by using the technique of subordination and introducing a novel generalized domain. This domain is obtained by taking the composition of trigonometric sine function and the well known curve called lemniscate of Bernoulli which is the image of open unit disc under a function g\u03be=1+\u03be. This domain is characterized by its pleasing geometry which exhibits symmetric about the real axis. For this newly defined subclass, we investigate the sharp upper bounds for its first four coefficients, as well as the second and third order Hankel determinants.<\/jats:p>","DOI":"10.3390\/axioms14030191","type":"journal-article","created":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T05:54:38Z","timestamp":1741154078000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Sharp Coefficients and Hankel Determinants for a Novel Class of Analytic Functions"],"prefix":"10.3390","volume":"14","author":[{"given":"Dong","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China"}]},{"given":"Adeel","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Hazara University Mansehra, Mansehra 21120, Pakistan"}]},{"given":"Huma","family":"Ikhlas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan"}]},{"given":"Saqib","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9038-1921","authenticated-orcid":false,"given":"Saima","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia"},{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia"}]},{"given":"Huo","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"M\u00e9moire sur certaines in\u00e9galit\u00e9s dans la th\u00e9orie des functions monog\u00e9nses et sur quelques propri\u00e9t\u00e9s nouvelles de ces fonctions dans le voisinage d\u2019unpoint singulier essentiel","volume":"35","year":"1909","journal-title":"Ann. Soc. Sci. Fenn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2307\/2007212","article-title":"Functions which map the interior of the unit circle upon simple regions","volume":"17","author":"Alexander","year":"1915","journal-title":"Ann. Math."},{"key":"ref_3","first-page":"940","article-title":"\u00dcber di\u00e9 Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln","volume":"138","author":"Bieberbach","year":"1916","journal-title":"Sitzungsberichte Preuss. Akad. Der Wiss."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02392821","article-title":"A proof of Bieberbach conjecture","volume":"154","author":"Branges","year":"1985","journal-title":"Acta Math."},{"key":"ref_5","unstructured":"Ma, W.C., and Minda, D. (1992). A unified treatment of some special classes of univalent functions. Proceedings of the Conference on Complex Analysis, International Press."},{"key":"ref_6","first-page":"101","article-title":"Radius of convexity of some subclasses of strongly starlike functions","volume":"19","author":"Stankiewicz","year":"1996","journal-title":"Zesz. Nauk. Politech. Rzesz. Mat."},{"key":"ref_7","first-page":"1427","article-title":"On coefficient estimates for a certain class of starlike functions","volume":"44","author":"Raina","year":"2015","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1007\/s13370-015-0387-7","article-title":"Starlike functions associated with a cardioid","volume":"27","author":"Sharma","year":"2016","journal-title":"Afr. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s41980-018-0127-5","article-title":"Radius problems for starlike functions associated with the sine function","volume":"45","author":"Cho","year":"2019","journal-title":"Bull. Iran. Math. Soc."},{"key":"ref_10","unstructured":"Kumar, S.S., and Arora, K. (2020). Starlike function associated with a petal shaped domain. arXiv."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s40840-020-00935-6","article-title":"Starlike and convex functions associated with a nephroid domain","volume":"44","author":"Wani","year":"2021","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_12","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_13","first-page":"018","article-title":"Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity","volume":"14","author":"Charlier","year":"2018","journal-title":"Symmetry Integr. Geom. Methods Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/mma.5347","article-title":"Painlev\u00e9 transcendents and the Hankel determinants generated by a discontinuous Gaussian weight","volume":"42","author":"Min","year":"2019","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"115221","DOI":"10.1016\/j.nuclphysb.2020.115221","article-title":"Painlev\u00e9 V and the Hankel determinant for a singularly perturbed Jacobi weight","volume":"961","author":"Min","year":"2020","journal-title":"Nucl. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1112\/plms\/s3-18.1.77","article-title":"On second Hankel determinant of mean univalent function","volume":"3","author":"Hayman","year":"1968","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_17","first-page":"1","article-title":"On third order Hankel determinant for some classes of univalent function","volume":"6","author":"Babalola","year":"2010","journal-title":"Inequal. Theory Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s00009-016-0829-y","article-title":"Third Hankel determinants for subclasses of univalent functions","volume":"14","author":"Zaprawa","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1007\/s40840-018-0683-0","article-title":"The bound of the Hankel determinant of the third kind for starlike functions","volume":"42","author":"Kwon","year":"2019","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1186\/1029-242X-2013-412","article-title":"Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli","volume":"2013","author":"Raza","year":"2013","journal-title":"J. Inequal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1160557","DOI":"10.1080\/23311835.2016.1160557","article-title":"Bounds on Hankel determinant for starlike and convex functions with respect to symmetric points","volume":"3","author":"Mishra","year":"2016","journal-title":"Cogent Math."},{"key":"ref_22","first-page":"211","article-title":"Upper bound of third Hankel determinant for a class of analytic functions","volume":"33","author":"Zhang","year":"2017","journal-title":"Pure Appl. Math."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Murugusundaramoorthy, G., and Bulboac\u0103, T. (2020). Hankel determinants for new subclasses of analytic functions related to a shell-shaped region. Mathematics, 8.","DOI":"10.3390\/math8061041"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s13398-020-00977-2","article-title":"Third Hankel determinant for univalent starlike functions","volume":"115","author":"Zaprawa","year":"2021","journal-title":"Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A Mat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1515\/math-2019-0132","article-title":"Hankel determinant of order three for familiar subsets of analytic functions related with sine function","volume":"17","author":"Arif","year":"2019","journal-title":"Open Math."},{"key":"ref_26","first-page":"8844814","article-title":"Applications of modified sigmoid functions to a class of starlike functions","volume":"2020","author":"Khan","year":"2020","journal-title":"J. Funct. Spaces"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.3934\/math.2022173","article-title":"Coefficient functional for a class of bounded turning functions related to modified sigmoid function","volume":"7","author":"Khan","year":"2021","journal-title":"AIMS Math."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shi, L., Khan, M.G., Ahmad, B., Mashwani, W.K., Agarwal, P., and Momani, S. (2021). Certain coefficient estimate problems for three-leaf-type starlike functions. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5040137"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Srivastava, H.M., Ahmad, Q.Z., Darus, M., Khan, N., Khan, B., and Zaman, N. (2019). Upper bound of the third Hankel determinant for a subclass of close-to-convex functions associated with the lemniscate of Bernoulli. Mathematics, 7.","DOI":"10.3390\/math7090848"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6365","DOI":"10.3934\/math.2022354","article-title":"Fekete-Szeg\u00f6 and Hankel inequalities for certain class of analytic functions related to the sine function","volume":"7","author":"Tang","year":"2022","journal-title":"AIMS Math."},{"key":"ref_31","first-page":"1","article-title":"Coefficient inequality for a function whose derivative has a positive real part","volume":"7","author":"Janteng","year":"2006","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1017\/S0004972717001125","article-title":"The sharp bound for the Hankel determinant of the third kind for convex functions","volume":"97","author":"Kowalczyk","year":"2018","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1007\/s11785-018-0819-0","article-title":"The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1\/2","volume":"13","author":"Lecko","year":"2019","journal-title":"Complex Anal. Oper. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1186\/s13660-021-02729-1","article-title":"A study of sharp coefficient bounds for a new subfamily of starlike functions","volume":"1","author":"Ullah","year":"2021","journal-title":"J. Inequal. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Arif, M., Barukab, O.M., Khan, S.A., and Abbas, M. (2022). The sharp bounds of Hankel determinants for the families of three-leaf-type analytic functions. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6060291"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Shi, L., Shutaywi, M., Alreshidi, N., Arif, M., and Ghufran, S.M. (2022). The sharp bounds of the third order Hankel determinant for certain analytic functions associated with an eight-shaped domain. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6040223"},{"key":"ref_37","first-page":"8356125","article-title":"Some sharp results on coefficient estimate problems for four-leaf-type bounded turning functions","volume":"2022","author":"Sunthrayuth","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Tang, H., Ahmad, A., Rasheed, A., Ali, A., Hussain, S., and Noor, S. (2023). Sharp coefficient and Hankel problems related to a symmetric domain. Symmetry, 15.","DOI":"10.3390\/sym15101865"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Raza, M., Riaz, A., Xin, Q., and Malik, S.N. (2022). Hankel determinants and coefficient estimates for starlike functions related to symmetric booth lemniscate. Symmetry, 14.","DOI":"10.3390\/sym14071366"},{"key":"ref_40","first-page":"30","article-title":"The Sharp bound of the third Hankel determinant for the inverse of bounded turning functions","volume":"4","author":"Kumar","year":"2023","journal-title":"Contemp. Math."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ahmad, A., Gong, J., Al-Shbeil, I., Rasheed, A., Hussain, S., and Ali, A. (2023). Analytic functions related to a balloon-shaped domain. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7120865"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Kumar, S., Breaz, D., Cot\u00eerl\u0103, L.-I., and \u00c7etinkaya, A. (2024). Hankel determinants of normalized analytic functions associated with hyperbolic secant function. Symmetry, 16.","DOI":"10.3390\/sym16101303"},{"key":"ref_43","first-page":"251","article-title":"Coefficient bounds for the inverse of a function with derivative in P","volume":"87","author":"Libera","year":"1983","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s40315-017-0229-8","article-title":"On the fourth coefficient of functions in the Carath\u00e9odory class","volume":"18","author":"Kwon","year":"2018","journal-title":"Methods Funct. Theory"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.crma.2015.03.003","article-title":"Bound for the fifth coefficient of certain starlike functions","volume":"353","author":"Ravichandran","year":"2015","journal-title":"Comptes Rendus Math."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Tang, H., Arif, M., Haq, M., Khan, N., Khan, M., Ahmad, K., and Khan, B. (2022). Fourth Hankel determinant problem based on certain analytic functions. Symmetry, 14.","DOI":"10.3390\/sym14040663"},{"key":"ref_47","first-page":"9991460","article-title":"A study of fourth-order Hankel determinants for starlike functions connected with the sine function","volume":"2021","author":"Zhang","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1515\/ms-2017-0354","article-title":"Investigation of the fifth Hankel determinant for a family of functions with bounded turnings","volume":"70","author":"Arif","year":"2020","journal-title":"Math. Slovaca"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/191\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:47:30Z","timestamp":1760028450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,5]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["axioms14030191"],"URL":"https:\/\/doi.org\/10.3390\/axioms14030191","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,3,5]]}}}