A Comprehensive subclass of analytic and bi-univalent functions associated with subordination (original) (raw)

Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations

Bulletin of the iranian mathematical society

A function is said to be bi-univalent in the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subordinations. Both the coefficient bounds and the techniques presented are new and we hope that this paper will inspire future researchers in applying our approach to other related problems.

Certain subclasses of analytic and bi-univalent functions

Applied Mathematics Letters, 2010

In the present paper, we introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk U := {z : z ∈ C and |z| < 1}, whose inverse has univalently analytic continuation to U. Among other results, bounds for the Taylor-Maclaurin coefficients |a 2 | and |a 3 | are found in our investigation.

Quasi subordination of bi-univalent functions involving convolution operator

PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science

In this article, the authors introduce two new subclasses of the class bi univalent functions in the open unit disk, which includes the convolution between Hurwitz-Lerch Zeta and the generalized derived operator and satisfies quasi subordination conditions. The coefficient estimates | 2 | and | 3 |were determined in these subclasses. These two operators were also applied to the subclasses and new results were obtained

On Some New Classes of Bi-univalent Functions

Journal of Applied Mathematics, Statistics and Informatics, 2018

In the present paper, we introduce and investigate two new subclasses QΣ(n; y;k) and BΣ(n;β;k) of bi-valent functions in the unit disk U. For functions belonging to the classes QΣ(n;y;k) and BΣ(n;β;k), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

On a Certain Subclasses of Bi-Univalent Functions

2016

In this paper, we introduce and study two new subclasses of biunivalent functions in the open unit disk U = {z : |z| < 1} and obtain bounds for the Taylor-Maclaurin coefficients |a2| and |a3|. The result presented in this paper generalize the recent work of Srivastava et al. [9]. 2010 Mathematics Subject Classification: 30C45.