Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214120230101A new subclass of bi-univalent functions associated with q-Chebychev polynomial18491856699710.22075/ijnaa.2022.28252.3845ENKavitha DDepartment of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, 605108, Tamilnadu, IndiaK. DhanalakshmiPG & Research Department of Mathematics, Theivanai Ammal College for Women (Autonomous), Villupuram, 605602, Tamilnadu, IndiaP. ManikandanDepartment of Mathematics, Anjalai Ammal Mahalingam Engineering College, Kovilvenni, 614403, Tamilnadu, IndiaJournal Article20220830In this article, using the concept of q-analogue, we define a new class of analytic functions associated with Chebyshev polynomial of second kind. Then with the help of symmetric q-Chebyshev polynomial, we introduce and estimating first two Maclaurin coefficients for new subclasses of analytic functions. Also as application of the results, we estimate the relevant connection to the famous classical Fekete- SzegĂ¶ inequality belonging to the class $\tilde{S}_{\Sigma}^{q}(\lambda,\gamma,s).$https://ijnaa.semnan.ac.ir/article_6997_de719169ca1301b4d19f1566c21adb8e.pdf