Results & Lemmas (3)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Theorem 2.1.
Theorem 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then |a2| ≤ eτ |br| p 2 |br| p |[φ(δ,…
Theorem 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then |a2| ≤ eτ |br| p 2 |br| p |[φ(δ, γ, λ, τ)b −2pθ] br2 −2qaθ2| and |a3| ≤ e2τ |br| τ [(1 −δ)(γ + 2) + δ(3λ −1)] + e2τb2r2 θ2 ,
Theorem 2.2.
Theorem 2.2. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r, µ ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then a3 −µa2 2 ≤
Theorem 2.2. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r, µ ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then a3 −µa2 2 ≤
Corollary 2.1.
Corollary 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then a3 −a2 2 ≤ e2τ |br| τ [(1…
Corollary 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, let f ∈A be in the family GΣ(δ, γ, λ, τ, r). Then a3 −a2 2 ≤ e2τ |br| τ [(1 −δ)(γ + 2) + δ(3λ −1)]. 3 Conclusion The fact that we can find many unique and ef- fective uses of a large variety of interesting func- tions and specific polynomial in Geometric Func- tion Theory provided the primary inspiration for our analysis in this article. The primary objec-
Definitions (1)
Def 2.1.
Definition 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, a function f ∈Σ is said to be in the family GΣ(δ, γ, λ, τ, r) if it satisfies…
Definition 2.1. For 0 ≤δ ≤1, γ ≥0, λ ≥1, 0 < τ ≤1 and r ∈R, a function f ∈Σ is said to be in the family GΣ(δ, γ, λ, τ, r) if it satisfies the WSEAS TRANSACTIONS on MATHEMATICS DOI: 10.37394/23206.2021.20.67 S. R. Swamy, Alina Alb Lupaş, Abbas Kareem Wanas, J. Nirmala E-ISSN: 2224-2880 631 Volume 20, 2021
Function classes studied:
Related Papers