Affiliation:
1. M. P. University of Agriculture and Technology Udaipur, Rajasthan INDIA
2. Department of Mathematics University of Rzeszów ul. Rejtana 16A 35-310 Rzeszów POLAND
Abstract
Abstract
In this note, we investigate the Fekete-Szegö problem for a class 𝓢𝒽 of functions f analytic in the open unit disc Δ = {z: |z| < 1} (and which is related to a shell-like curve associated with Fibonacci numbers) satisfying the conditions that
f
(
0
)
=
0
,
f
′
(
0
)
=
1
and
z
f
′
(
z
)
f
(
z
)
≺
1
+
τ
2
z
2
1
−
τ
z
−
τ
2
z
2
(
z
∈
Δ
)
,
$$f(0) = 0,\qquad f'(0) = 1\qquad {\text{and}}\qquad \frac{{zf'(z)}}{{f(z)}} \prec \frac{{1 + {\tau ^2}{z^2}}}{{1 - \tau z - {\tau ^2}{z^2}}}\quad (z \in \Delta ),$$
where ≺ denotes the subordination and the number
τ
=
(
1
−
5
)
/
2
$\tau = (1 - \sqrt 5 )/2$
is such that |τ| fulfils the golden section of the segment [0,1].
Cited by
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