On The Third Logarithmic Coefficient Estimates for Certain Generalized Subclass of Close-to-Convex Functions

Huzaifah Dzubaidi; Shaharuddin Cik Soh

Authors

Huzaifah Dzubaidi Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
Shaharuddin Cik Soh Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

Keywords:

Univalent functions, analytic functions, close-to-convex functions, logarithmic coefficients

Abstract

In this paper, we introduce a new class of generalized close-to-convex functions, which satisfies the following condition, where and . The third logarithmic coefficient estimates are considered, and we obtain sharp inequality for the class. Our results extend and unify previous work on starlike, convex, and close-to-convex functions under representation theorem.