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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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.

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