Certain classes of bi-univalent functions associated with the Horadam polynomials

Abstract

In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.

Bi-univalent Function Subclasses Subordinate to Horadam Polynomials

“…Further by letting ν = 1, we obtain Corollary 2.3 of Magesh et al [17], which is also stated as Corollary 1 in Orhan et al [19]. Also, we get Corollary 2 of Orhan et al [19], if we let ν = 0 instead of ν = 1. ii) Taking ν = 1 in Theorem 2.1, we get Corollary 2.4 of Swamy and Sailaja [28].…”

“…|1 − δ| ≤ Q |1−δ| |(6(1−γ)+(τ −γ)(1−4γ)+2τ 2 )(bκ) 2 −4(1+τ −γ) 2 (pbκ 2 +qa)| ; |1 − δ| ≥ Q 3 ,whereQ 3 = 1 3(2 + τ − γ) 6(1 − γ) + (τ − γ)(1 − 4γ) + 2τ 2 − 4(1 + τ − γ) 2 pbκ 2 + qa b 2Remark Allowing γ = τ = 1 in Corollary 3.3, we obtain a result of Magesh et al[17, Corollary 2.3], which is also stated as Corollary 1 in Orhan et al[19].…”

“…from which we conclude (2.3) with J as in (2.4). Remark 2.1. i) Taking τ = 1 in Theorem 2.1, we get a result of Orhan et al [19,Theorem 1]. Further by letting ν = 1, we obtain Corollary 2.3 of Magesh et al [17], which is also stated as Corollary 1 in Orhan et al [19].…”

“…Remark 1.3. i) When τ = 1, the family SU 1 σ (ν, κ) was examined by Orhan et al [19]. ii) When τ = 1, the family ST 1 σ (γ, µ, κ) was investigated by Swamy and Sailaja [28].…”

CERTAIN SUBCLASS OF BI-UNIVALENT FUNCTIONS RELATED TO HORADAM POLYNOMIALS ASSOCIATED WITH q-DERIVATIVE

“…(i) If we take q → 1 in our Theorems, we have the corresponding results for the family G * (α, x) of bi-univalent functions which was considered by Orhan [7].…”