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

Abstract

The object of this article is to explore a τ-pseudo-ν-convex κ-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates of functions in the defined family. The classical Fekete–Szegö inequalities for functions in the defined τ-pseudo-ν-convex family is also estimated. Furthermore, we present some of the special cases of the main results. Relevant connections with those in several earlier works are also pointed out. Our study in this paper is also motivated by the symmetry nature of κ-fold symmetric bi-univalent functions in the defined class.

Coefficient Bounds for a New Families of m-Fold Symmetric Bi-Univalent Functions Defined by Bazilevic Convex Functions

“…For a brief history and interesting examples in the family Σ see the pioneering work on this subject by Srivastava et al [25], which actually revived the study of bi-univalent functions in recent years. In a considerably large number of sequels to the aforementioned work of Srivastava et al [25], several different sub families of the bi-univalent function family Σ were introduced and studied analogously by the many authors (see, for example, [1,2,3,5,9,10,11,15,19,23,28,29,30,33]).…”

A New Pseudo-Type κ-Fold Symmetric Bi-Univalent Function Class

“…Initial coefficient bounds for new subfamilies of σ κ were determined in [20]. The Fekete-Szegö (FS) issue |d 2m+1 − δd 2 m+1 |, δ ∈ R (see [21]) for certain special families of σ κ was examined by Swamy et al [22,23]; and another spe-cial family of σ κ satisfying certain subordination conditions was examined by Aldawish et al [24]; initial coefficients estimates for elements belonging to certain new families of σ κ were obtained by Breaz and Cotîrlȃ in [25] (see [26][27][28]), indicating the developments in this domain.…”

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

“…For a brief history and interesting examples in the family Σ see the pioneering work on this subject by Srivastava et al [24], which actually revived the study of bi-univalent functions in recent years. In a considerably large number of sequels to the aforementioned work of Srivastava et al [24], several different sub families of the bi-univalent function family Σ were introduced and studied analogously by the many authors (see, for example, [2,3,5,11,15,18,22,27,28,30,33]).…”