{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:56:15Z","timestamp":1760147775931,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"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>Motivated by the recent work on symmetric analytic functions by using the concept of Faber polynomials, this article introduces and studies two new subclasses of bi-close-to-convex and quasi-close-to-convex functions associated with Janowski functions. By using the Faber polynomial expansion method, it determines the general coefficient bounds for the functions belonging to these classes. It also finds initial coefficients of bi-close-to-convex and bi-quasi-convex functions by using Janowski functions. Some known consequences of the main results are also highlighted.<\/jats:p>","DOI":"10.3390\/sym15030604","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T05:29:37Z","timestamp":1677475777000},"page":"604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Faber Polynomial Coefficient Estimates for Janowski Type bi-Close-to-Convex and bi-Quasi-Convex Functions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7950-8450","authenticated-orcid":false,"given":"\u015eahsene","family":"Alt\u0131nkaya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Beykent University, Istanbul 34500, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6178-8538","authenticated-orcid":false,"given":"Qin","family":"Xin","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7855-508X","authenticated-orcid":false,"given":"Fairouz","family":"Tchier","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8940-0569","authenticated-orcid":false,"given":"Sarfraz Nawaz","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1123-8578","authenticated-orcid":false,"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"ref_1","unstructured":"Duren, P.L. (1983). Grundehren der Mathematischen Wissenschaften, Springer."},{"key":"ref_2","unstructured":"Goodman, A.W. (1983). Univalent Functions, Mariner."},{"key":"ref_3","unstructured":"Hayman, W.K. (1967). 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