Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Starlikeness of the generalized integral transform using duality techniques (1411.5217v1)

Published 19 Nov 2014 in math.CV

Abstract: For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}{\beta}\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,} e{i\phi}(\dfrac{}{}(1!-!\alpha!+!2\gamma)!({f}/{z})\delta +(\alpha!-!3\gamma!+!\gamma[\dfrac{}{}(1-{1}/{\delta})({zf'}/{f})+ {1}/{\delta}(1+{zf''}/{f'})]).\ .\dfrac{}{}({f}/{z})\delta !({zf'}/{f})-\beta)>0, \end{align*} where $\phi\in\mathbb{R}$ and $|z|<1$, is taken into consideration. The class $\mathcal{S}\ast_s(\zeta)$ be the subclass of the univalent functions, defined by the analytic characterization ${\rm Re}{\,}({zf'}/{f})>\zeta$, for $0\leq \zeta< 1$, $0<\delta\leq\frac{1}{(1-\zeta)}$ and $|z|<1$. The admissible and sufficient conditions on $\lambda(t)$ are examined, so that the generalized and non-linear integral transforms \begin{align*} V{\lambda}\delta(f)(z)= (\int_01 \lambda(t) ({f(tz)}/{t})\delta dt){1/\delta}, \end{align*} maps the function from $\mathcal{W}_{\beta}\delta(\alpha,\gamma)$ into $\mathcal{S}\ast_s(\zeta)$. Moreover, several interesting applications for specific choices of $\lambda(t)$ are discussed, that are related to some well-known integral operators.

Summary

We haven't generated a summary for this paper yet.