Duality for convolution on subclasses of analytic functions and weighted integral operators
نویسندگان
چکیده
Abstract In this article, we investigate a class of analytic functions defined on the unit open disc U = { z : ∣ < 1 } {\mathcal{U}}=\left\{z:| z| \lt 1\right\} , such that for every f ∈ mathvariant="script">P α ( β , γ ) f\in {{\mathcal{P}}}_{\alpha }\left(\beta ,\gamma ) > 0 \alpha \gt 0 ≤ 0\le \beta \le 1 0\lt \gamma and | inequality xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> mathvariant="normal">Re ′ + − accent="true">″ {\rm{Re}}\left\{\frac{f^{\prime} \left(z)+\frac{1-\gamma }{\alpha }z{f}^{^{\prime\prime} }\left(z)-\beta }{1-\beta }\right\}\gt holds. We find conditions numbers ,\beta ⊆ S P λ )\subseteq SP\left(\lambda π 2 \lambda \in \left(-\frac{\pi }{2},\frac{\pi }{2}) where denotes set all -spirallike functions. also make use Ruscheweyh’s duality theory to derive real-valued function φ \varphi so integral operator V {V}_{\varphi }(f) maps into provided is non-negative normalized ∫ t mathvariant="normal">d \left({\int }_{0}^{1}\varphi \left(t){\rm{d}}t=1) . }(f)\left(z)=\underset{0}{\overset{1}{\int }}\varphi \left(t)\frac{f\left(tz)}{t}{\rm{d}}t.
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2023
ISSN: ['0420-1213', '2391-4661']
DOI: https://doi.org/10.1515/dema-2022-0168