Résumé:
In the present paper we determine sharp lower bounds of
the real part of the ratios of harmonic univalent meromorphic functions
to their sequences of partial sums.
Let H denote the class of functions f that are harmonic univalent and
sense-preserving in U =; fz : jzj > 1g which are of the form
f(z) = h(z) + g(z) ;
where
h(z) = z +
1X
n=1
anzn ; g(z) =
1X
n=1
bnzn.
Now, we de ne the sequences of partial sums of functions f of the form
fs(z) = z +
Xs
n=1
anzn + g(z);
e fr(z) = g(z) +
Xr
n=1
bnzn;
fs;r(z) = z +
Xs
n=1
anzn +
Xr
n=1
bnzn:
In the present paper we will determine sharp lower bounds for Re
n
f(z)
fs(z)
o
;
Re
n
fs(z)
f(z)
o
; Re
n
f(z)
e fr(z)
o
; Re
n e fr(z)
f(z)
o
; Re
n
f(z)
fs;r(z)
o
, Re
n
fs;r(z)
f(z)
o
:
