Abstract
In this paper, we find upper bounds for the first two Taylor-Maclaurin || and
|| for two new families
, ; and
∗
, ; of holomorphic and -fold
symmetric bi-univalent functions associated with the Bazilevic convex functions defined
in the open unit disk . Further, we point out several certain special cases for our results.
Results & Lemmas (7)
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Lemma 1.1 · coeff
Lemma 1.1 [3]. If ℎ∈[, then | '| ≤2 for each ] ∈ℕ, where [ is the family of all all functions ℎ holomorphic in for which ^Y6ℎ 7 > 0,…
Lemma 1.1 [3]. If ℎ∈[, then |\'| ≤2 for each ] ∈ℕ, where [ is the family of all all functions ℎ holomorphic in for which ^Y6ℎ 7 > 0, ∈, where ℎ = 1 + \ + \ + ⋯, ∈. 2. Coefficient Estimates for the Function Family _` a, b; c
Theorem 2.1.
Theorem 2.1. Let ∈, ; 0 < ≤1, 0 ≤ ≤1, 0 ≤ ≤1, ∈ℕ be given by (1.3). Then || ≤ 2 op2 q 1 − 2 + + 2 2 + 1 + 1…
Theorem 2.1. Let ∈ , ; 0 < ≤1, 0 ≤
≤1, 0 ≤ ≤1, ∈ℕ be given by (1.3). Then || ≤ 2 op2 q 1 −
2 + + 2
2 + 1 + 1 −
−1 2 + + r + 1 −J 1 −
+ +
+ 1K p 2.3 and || ≤ 4 J 1 −
+ +
+ 1K +
Corollary 2.1.
Corollary 2.1. Let ∈, ; 0 < ≤1,0 ≤ ≤1, 0 ≤ ≤1 be given by (1.1). Then
Corollary 2.1. Let ∈ , ; 0 < ≤1,0 ≤
≤1, 0 ≤ ≤1 be given by (1.1). Then
Theorem 1 · coeff
Theorem 1]. 3. Coefficient Estimates for the Function Family _` ∗ a, b;
Theorem 1]. 3. Coefficient Estimates for the Function Family _` ∗ a, b; {
Theorem 3.1.
Theorem 3.1. Let ∈
Theorem 3.1. Let ∈
Corollary 3.1.
Corollary 3.1. Let ∈ ∗, ; 0 ≤ < 1, 0 ≤ ≤1, 0 ≤ ≤1 be given by (1.1). Then || ≤o 2 1 − z 1 − 2 + + 6 + 1 − −1 2 1…
Corollary 3.1. Let ∈ ∗
, ; 0 ≤ < 1, 0 ≤
≤1, 0 ≤ ≤1 be given by (1.1). Then || ≤o 2 1 − z 1 −
2 + + 6
+ 1 −
−1 2 1 + + z
Theorem 2
Theorem 2]. 4. Conclusion The present study has introduced a new subfamilies, ; and
Theorem 2]. 4. Conclusion The present study has introduced a new subfamilies , ; and
Definitions (2)
Def 2.1.
Definition 2.1. A function ∈D given by (1.3) is said to be in the family
Definition 2.1. A function ∈D given by (1.3) is said to be in the family
Def 3.1.
Definition 3.1. A function ∈D given by (1.3) is said to be in the family
Definition 3.1. A function ∈D given by (1.3) is said to be in the family
Function classes studied:
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