Certain classes of bi-univalent functions with bounded boundary variation

Abstract

In their pioneering work dated 2010 on the subject of bi-univalent functions, Srivastava et al. actually revived the study of the coefficient problems involving bi-univalent functions in recent years. Inspired by the pioneering work of Srivastava et al., there has been triggering interest to study the coefficient problems for many different subclasses of bi-univalent functions. Motivated largely by a number of sequels to the investigation by Srivastava et al., in this paper, we consider certain classes of bi-univalent functions to obtain the estimates of their second and third Taylor-Maclaurin coefficients. Further, certain special cases are also indicated. Some interesting remarks about the results presented here are also discussed.

Bi-univalent properties for certain class of Bazilevič functions defined by convolution and with bounded boundary rotation

“…The results in Corollary 9 correct the results obtained by Orhan et al [11] [Theorem 2.11, with γ = 1. ].…”

“…We note that by putting different values for h, α, β, k, λ, and ρ, in the above definition, we have: [11], with γ = 1);…”

Initial estimates for certain subclasses of bi-univalent functions with $κ-$Fibonacci numbers

“…A function f ∈ A is said to be bi-univalent in D if both f and f −1 are univalent in D. Let Σ denote the class of bi-univalent functions in D given by (1.1). Various subclasses of 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 several recent investigations (see, for example, [1,2,3,6,7,8,13,21,22,23,24,30,31,32,33,34,35,36,37,38] and references therein). However, the problem is to find the coefficient bounds on |a n | (n = 3, 4, .…”

Certain classes of bi-univalent functions related to Shell-like curves connected with Fibonacci numbers

“…Motivated by works of Ali et al [1], Güney et al [10] and Orhan et al [13], we introduce the following new subclasses of bi-univalent functions, as follows.…”