On a new subclass of bi-univalent functions satisfying subordinate conditions

Abstract

In the present investigation, we find estimates on the coefficients |a2| and |a3| for functions in the function class SΣ (λ,φ) . The results presented in this paper improve or generalize the recent work of Magesh and Yamini

On a new subclass of bi-univalent functions satisfying subordinate conditions

“…Remark 1. Taking = 1 in the above Theorem 1 and Corollaries 1, 2, we obtain the results of Altinkaya and Yalcin [1].…”

“…( ) and K ( ) ; they found non-sharp estimates for the initial coe¢ cients. Recently, motivated substantially by the aforementioned pioneering work on this subject by Srivastava et al [21], many authors investigated the coe¢cient bounds for various subclasses of bi-univalent functions (see, for example, [1], [3], [12], [15], [17], [22], [23] and [24]). Not much is known about the bounds on the general coe¢ cient ja n j for n = 4: In the literature, there are only a few works determining the general coe¢ cient bounds for ja n j for the analytic bi-univalent functions (see, for example, [2], [4], [13], [25]).…”

New Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials

“…According to the "Koebe One-Quarter Theorem" [13] each function from has an inverse 12 , which fulfills [36] on the subject, the large number of works associated with the subject have been presented (see, for example [1,2,4,5,8,9,10,11,14,17,18,21,22,25,28,29,30,31,32,33,34,35,37,38,39,40,41]). We see that the set A is not empty.…”

Coefficient Estimates of Some Classes of Univalent Functions using Subordination Principle

“…3 Altinkaya and Yalçin [1] gave the coefficient estimate of a class of bi-univalent functions using the Schwarz function…”