S.O. Olatunji and E.J. Dansu, On neighbourhoods of analytic functions defined by using modified sigmoid function associated with conic domain, Volume 2017, Number 1, Pages 41-47, 2017
Abstract: The neighbourhood of $N_\delta(f)$ for function $f_\gamma\in k$-$T_n^s[A,B]$ whose geometric condition satisfy
$R\left(\frac{(B-1)\frac{D^{n+1}f_\gamma(z)}{D^nf_\gamma(z)}-(A-1)}{(B+1)\frac{D^{n+1}f_\gamma(z)}{D^nf_\gamma(z)}-(A+1)}\right)> k\left|\frac{(B-1)\frac{D^{n+1}f_\gamma(z)}{D^nf_\gamma(z)}-(A-1)}{(B+1)\frac{D^{n+1}f_\gamma(z)}{D^nf_\gamma(z)}-(A+1)}-1\right|$
where $k\geq 0$, $n\in N_0$, $-1\leq B<A\leq 1$ and $\lim_{s\rightarrow \infty}\gamma(s)=1$ is considered.
Key words: Starlike Function; Convex Function; Analytic Function; Modified Sigmoid Function; Conic Domain.
Full text: PDF
Full file: XML
How to cite this article:
S.O. Olatunji and E.J. Dansu, On neighbourhoods of analytic functions defined by using modified sigmoid function associated with conic domain, International Journal of Advances in Mathematics, Volume 2017, Number 1, Pages 41-47, 2017.