Continue from this paper
Indexing is not verification. Extracted statements should be checked against the source.
Abstract
In terms of the Dziok-Srivastava operator, we introduce and study some new classes
of strongly starlike functions. Certain properties of these subclasses are studied.
Results & Lemmas (4)
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 1.
Theorem 1. Mα1+1(β, γ) ⊂Mα1(β, γ) for α1 > 1 −γ and 0 ≤γ < 1.
Theorem 1. Mα1+1(β, γ) ⊂Mα1(β, γ) for α1 > 1 −γ and 0 ≤γ < 1.
Theorem 2.
Theorem 2. Pα1+1(β, γ) ⊂Pα1(β, γ) for α1 > 1 −γ and 0 ≤γ < 1.
Theorem 2. Pα1+1(β, γ) ⊂Pα1(β, γ) for α1 > 1 −γ and 0 ≤γ < 1.
Theorem 3.
Theorem 3. Let v>−γ and 0 ≤γ < 1. If f(z)∈Mα1(β, γ) with z(Hq,s(α1)Jvf(z))′/ Hq,s(α1)Jvf(z) ̸= γ for all z ∈E, then Jvf(z) ∈Mα1(β, γ),…
Theorem 3. Let v>−γ and 0 ≤γ < 1. If f(z)∈Mα1(β, γ) with z(Hq,s(α1)Jvf(z))′/ Hq,s(α1)Jvf(z) ̸= γ for all z ∈E, then Jvf(z) ∈Mα1(β, γ), where Jvf(z) is given by Jvf(z) = v + 1 zv Z z 0 tv−1f(t)dt (v > −1; f(z) ∈A). (2.3)
Theorem 4.
Theorem 4. Let v>−γ and 0≤γ <1. If f(z)∈Pα1(β, γ) and 1+z(Hq,s(α1)Jvf(z))′′/ (Hq,s(α1)Jvf(z))′ ̸= γ for all z ∈E, then Jvf(z) ∈Pα1(β, γ).
Theorem 4. Let v>−γ and 0≤γ <1. If f(z)∈Pα1(β, γ) and 1+z(Hq,s(α1)Jvf(z))′′/ (Hq,s(α1)Jvf(z))′ ̸= γ for all z ∈E, then Jvf(z) ∈Pα1(β, γ).
Function classes studied:
Related Papers