Subclasses of bi-univalent functions defined by convolution

Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

“…In this work, we introduce a new subclass of bi-univalent functions which is defined by Hadamard product and find upper bounds for the second and third coefficients for functions in this new subclass. Besides, the estimates on the coefficients |a 2 | and |a 3 | presented in this work would generalize and improve some of results of Aouf et al [4], Bulut [8], Ç aglar et al [9], El-Ashwah [12], Frasin and Aouf [14], Murugusundaramoorthy [18], Orhan et al [19], Porwal and Darus [20], Prema and Keerthi [21], Srivastava et al [24], Srivastava et al [25] and related works in this literature.…”

“…Coefficient Estimates for a New Subclass 93 Remark 3.14. For m = β = 0, µ = 1, Ω(z) = z 1−z and h(z) = 1+(1−2γ)z 1−z, where 0 ≤ γ < 1, the class NP λ,µ Σ (m, β, ν, ϕ; h, Θ, Ω) reduce to a class B Σ (Θ, γ, λ) which defined by El-Ashwah[12, Definition 2].…”

Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product

“…For a brief history and interesting examples of functions in the class Σ, see [2] (see also [3]). In fact, the aforecited work of Srivastava et al [2] essentially revived the investigation of various subclasses of the bi-univalent function class Σ in recent years; it was followed by such works as those by Tang et al [4], El-Ashwah [5], Frasin and Aouf [6], Aouf et al [7], and others (see, e.g., [2,[8][9][10][11][12][13][14][15]). …”

Coefficient bounds for bi-univalent classes defined by Bazilevič functions and convolution

“…2Þ ( see [2]); (3) W j;1Àq;2;0 ðf à hÞ ¼ W j;q ðf à hÞ ðf ; h 2 P ; j ! 1 and 0 q\1Þ (see [8] and [12]); (4) W 1;1Àq;2;0 ðf à z 1Àz Þ ¼ W q ðf Þ ðf 2 P and 0 q\1Þ ( see [22] and [11]); (5) W r;1Àq;2;0 ðf à z 1Àz Þ ¼ W q;r ðf Þ ðf 2 P ; r ! 0 and 0 q\1Þ (see [9]).…”