Document Type : Research Paper

Authors

• Ranjan Suresh Khatu ¹
• Uday H. Naik ²
• Amol B. Patil ³

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

Abstract

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.

Keywords

• Analytic function
• Univalent function
• Convolution
• Coefficient bounds
• Bi-univalent function