The Study of the New Classes of m-Fold Symmetric bi-Univalent Functions

Abstract

In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f−1 are m-fold symmetric holomorphic functions in the open unit disk. We denote these classes of functions by FSΣ,mp,q,s(d), FSΣ,mp,q,s(e) and FSΣ,mp,q,s,h,r. As the Fekete-Szegö problem for different classes of functions is a topic of great interest, we study the Fekete-Szegö functional and we obtain estimates on coefficients for the new function classes.

Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

“…Following the works of Murugusundaramoorthy et al [13], one can extend the study for results on Hölder inequalities, partial sums and subordination for f ∈ SI m (ξ, η, δ). We also consider for future study the papers [17][18][19][20].…”

Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions

“…There have been many papers in recent years on analytic and bi-univalent functions, e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

“…The momentum on investigations of functions in certain subfamilies of σ κ was gained in recent years due to the paper [16] and it has led to a large number of papers on subfamilies of σ κ [17][18][19][20]. Inspired by these works, many researchers have investigated several interesting subfamilies of σ κ and found non-sharp estimates on initial coefficients and the Fekete-Szegö functional problem |d 2κ+1 − δd 2 κ+1 |, δ ∈ [21] of functions belonging to these subfamilies (see, for example [22][23][24][25]) and this continued to appear in [26,27], showing the developments in the subject area of this paper.…”