Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions

Abstract

In this work, we introduce and investigate a subclass Hh,p ?m(?,?) of analytic and bi-univalent functions when both f(z) and f-1(z) are m-fold symmetric in the open unit disk U. Moreover, we find upper bounds for the initial coefficients |am+1| and |a2m+1| for functions belonging to this subclass Hh,p ?m(?,?). The results presented in this paper would generalize and improve those that were given in several recent works.

Bounds for initial MacLaurin coefficients of a subclass of bi-univalent functions associated with subordination

“…For a brief history and interesting examples of functions in the class , see [15]. In fact that this widely-cited work by Srivastava et al [15] actually revived the study of analytic and bi-univalent functions in recent years and that it has led to a ‡ood of papers on the subject by (for example) Srivastava et al [6,16,17,18,19,20,21,22,23,24,25,26], and others [10,11,14,27]. The co-e¢ cient estimate problem i.e.…”

Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

“…We indicate by Σ the family of bi-univalent functions in U given by (1). In fact, Srivastava et al [22] have actually revived the study of holomorphic and bi-univalent functions in recent years, it was followed by such works as those by Frasin and Aouf [8], Murugusundaramoorthy et al [13], Srivastava and Wanas [25] and others (see, for example [1,3,4,5,9,10,11,12,15,16,17,18,19,20,21,23,14,24,26,27,28,29,30,31,32,33]). We notice that the family Σ is not empty.…”

Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions

“…Recently, many authors investigated bounds for the various subclasses of k-fold symmetric bi-univalent functions (see [1,2,4,10,11,13]). This work aims to introduce the new subclasses N Σ k (µ, α, τ ) and N Σ k (µ, β, τ ) of Σ k and find estimates of the coefficients |a k+1 | and |a 2k+1 | for functions in each of these new subclasses.…”