Estimation on initial coefficient bounds of generalized subclasses of bi-univalent functions

Document Type : Research Paper


1 Department of Mathematics, Arts, Commerce and Science College, Lanja-416701, India

2 Department of Mathematics, Willingdon College, Sangli-416415, India

3 Department of First Year Engineering, AISSMS College of Engineering, Pune-411001, India


In the present investigation, we introduce the two subclasses $S^{\alpha}_{\Sigma}(\gamma, \rho, \lambda, \mu, \xi, \delta)$ and $S_{\Sigma}(\gamma, \rho, \lambda, \mu, \xi, \delta;\beta)$ of normalized analytic bi-univalent functions defined in the open unit disk and associated with the Ruscheweyh's operator. Further, we obtain bounds for the second and third Taylor-Maclaurin coefficients of the functions belong to these subclasses. We also provide relevant connections with earlier investigations of other researchers.


Volume 13, Issue 2
July 2022
Pages 989-997
  • Receive Date: 27 June 2021
  • Revise Date: 26 January 2022
  • Accept Date: 06 February 2022
  • First Publish Date: 14 April 2022