Hindawi Abstract and Applied Analysis Volume 2019, Article ID 6947020, 6 pages https://doi.org/10.1155/2019/6947020 Research Article Certain Subclasses of Bi-Close-to-Convex Functions Associated with Quasi-Subordination Gurmeet Singh ,1 Gurcharanjit Singh,2 and Gagandeep Singh 3 Principal, Patel Memorial National College, Rajpura, Punjab, India Research Scholar, Department of Mathematics, Punjabi University, Patiala, Punjab, India Department of Mathematics, Majha College for Women, Tarn Taran Sahib, Punjab, India Correspondence should be addressed to Gagandeep Singh;
[email protected] Received 13 January 2019; Accepted 7 March 2019; Published 1 April 2019 Academic Editor: Luigi Rodino Copyright © 2019 Gurmeet Singh et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the present investigation, we introduce certain new subclasses of the class of biunivalent functions in the open unit disc �={�: |�| < 1} defned by quasi-subordination. We obtained estimates on the initial coefcients |�2| and |�3| for the functions in these subclasses. Te results present in this paper would generalize and improve those in related works of several earlier authors. ��� (�) 1. Introduction and Preliminaries �={�:�∈�, ( )>0,�(�) ∈�∗;� Re � (�) Let � be the class of functions of the form ∞ � � (�) =�+∑ ��� (1) ∈�}, the class of close-to-convex functions. �=2 which are analytic in the open unit disc �={�:|�|<1}. � { (��� (�)) Further, let � be the class of functions �(�) ∈ � and univalent �1 = {�:�∈�,Re ( )>0,ℎ(�) ∈�;� in �. ℎ� (�) { By �, we denote the class of bounded or Schwarz func- tions �(�) satisfying �(0) = 0 and |�(�)| ≤ 1 which are � } analytic in the unit disc and of the form ∈�} , the class of quasi-convex functions.