Abstract
In this paper, making use of certain linear operators, we consider
Fekete-Szeg¨o problem for some subclasses of analytic functions.
2010 Mathematics Subject Classification: Primary 05A30, 30C45; Secondary
11B65, 47B38.
Results & Lemmas (5)
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Lemma 1.
Lemma 1. If a function p(z) ∈P then for n ≥1 i) |cn| ≤ 2 (8) ii) |c2 −c2 1 2 | ≤ 2 −c2 1 2. (9)
Lemma 1. If a function p(z) ∈P then for n ≥1 i) |cn| ≤ 2 (8) ii) |c2 −c2 1 2 | ≤ 2 −c2 1 2 . (9)
Theorem 2.
Theorem 2. Let δ ∈(o, 1], α > 1, λ ≥0. If f (z) ∈R (P, α, λ) and µ ∈C. Then a3 −µa2 2 ≤δ 2α+1 3 (1 + λ) max 1, δ 23α−1 (2 + λ)2…
Theorem 2. Let δ ∈(o, 1], α > 1, λ ≥0. If f (z) ∈R (P, α, λ) and µ ∈C. Then a3 −µa2 2 ≤δ 2α+1 3 (1 + λ) max 1, δ 23α−1 (2 + λ)2 −µ32α+1 (1 + λ)
Theorem 3.
Theorem 3. Let δ ∈(0, 1], α > 1, β > 0, λ ≥0. If f (z) ∈R (Q, α, λ) and µ ∈C. Then a3 −µa2 2 ≤δ 2 (α + β)3 3 (β + 1)2 (α + β + 2λ) max ( 1,…
Theorem 3. Let δ ∈(0, 1], α > 1, β > 0, λ ≥0. If f (z) ∈R (Q, α, λ) and µ ∈C. Then a3 −µa2 2 ≤δ 2 (α + β)3 3 (β + 1)2 (α + β + 2λ) max ( 1, δ |η (α, β)| 2 (α + β)3 (β + 1) (α + β + λ)2 ) , where η (α, β) = 2 (α + β)3 (β + 1) (α + β + λ)2 −3µ (α + β)2
Theorem 4.
Theorem 4. Let δ ∈(0, 1], α > 1, λ ≥0. If the function f (z) given by (1) is in the class R (P, α, λ) and µ is real parameter then a3 −µa2…
Theorem 4. Let δ ∈(0, 1], α > 1, λ ≥0. If the function f (z) given by (1) is in the class R (P, α, λ) and µ is real parameter then a3 −µa2 2 ≤
Theorem 5.
Theorem 5. Let δ ∈(0, 1], α > 1, β > 0, λ ≥0. If the function f (z) given by (1) is in the class R (Q, α, λ) and µ is real then a3 −µa2 2 ≤…
Theorem 5. Let δ ∈(0, 1] , α > 1, β > 0, λ ≥0. If the function f (z) given by (1) is in the class R (Q, α, λ) and µ is real then a3 −µa2 2 ≤
Function classes studied:
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