Some extensions of coefficient problems for bi-univalent Ma-Minda starlike and convex functions

Abstract

Motivated by the works of H.M. Srivastava et al. [7], we introduce and investigate two new general subclasses HT (?,?,?), h,pHT (?) of bi-starlike and bi-convex of Ma-Minda type functions. Bounds on the first two coefficients |a2| and |a3| for functions in HT (?,?,?), h,pHT (?) are given. The results here generalize and improve the corresponding earlier works done by Ali et al.[1] and Brannan et al.[2].

Initial bounds for certain classes of bi-univalent functions defined by Horadam polynomials

“…In 2010, Srivastava et al [20] revived the study of bi-univalent functions by their pioneering work on the study of coefficient problems. Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1.1) were found in the recent investigations (see, for example, [1,2,3,4,5,6,9,10,11,12,13,14,15,16,17,18,19,21,22,23]) and including the references therein. The afore-cited all these papers on the subject were actually motivated by the work of Srivastava et al [20].…”

On a New Ma-Minda Class of Analytic Functions Created by a Roulette Curve Formula

“…Many researchers defined special cases by suggesting a specific formula of F such as Janowski function [7], integral operator [8], 1 + sin(ξ) function [9], close to convex [10], quasi-subordination classes [11], τ-class [12], Quantum classes (see [13,14]), Nephroid domain with parametric function [15], exponential function [16], lemniscate of Bernoulli [17], MMT starlike and convex of complex order [18], bi-pseudo-starlike functions [19,20], fractional calculus [21], linear operator [22], conformable fractional operator [23] and other combination and convolution classes which can be located in [24][25][26][27][28].…”