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

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.

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