TY - JOUR AU - CHO, NAK EUN AU - KIM, JI A PY - 1994/09/01 Y2 - 2024/03/29 TI - CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 25 IS - 3 SE - Papers DO - 10.5556/j.tkjm.25.1994.4452 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4452 SP - 247-256 AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">Let </span><span style="font-size: 19.000000pt; font-family: 'TimesNewRomanPS'; font-style: italic;">$\Sigma_p$ </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">denote the class of functions of the form </span></p><p><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">\[f(z)=\frac{a_{-1}}{z}+\sum_{k=1}^\infty a_kz^k \quad (a_k\ge 0, a_{-1}&gt;0)\]</span></p><div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">which are analytic in the annulus $</span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPS'; font-style: italic;">D </span><span style="font-size: 17.000000pt; font-family: 'TimesNewRomanPSMT';">=\</span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">{z |0</span><span style="font-size: 13.000000pt; font-family: 'ArialMT';">&lt; |</span><span style="font-size: 14.000000pt; font-family: 'ArialMT';">z|</span><span style="font-size: 13.000000pt; font-family: 'ArialMT';">&lt;</span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">1\}$. Let $\Sigma_{</span><span style="font-size: 8.000000pt; font-family: 'TimesNewRomanPSMT';">p,1}$ </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">and </span><span style="font-size: 8.000000pt; font-family: 'TimesNewRomanPSMT';"><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">$\Sigma_{</span>p,2}$ </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">denote subclasses of $\Sigma_<span style="font-size: 8.000000pt; font-family: 'TimesNewRomanPSMT';">p$</span></span> <span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">satisfying $f(z_0)=1/z_0$ and $f'(z_0)=-1/z^2_0$ ($-1&lt;z_0&lt;1$, $z_0 eq 0$), respectively. Properties of certain subclasses of </span><span style="font-size: 8.000000pt; font-family: 'TimesNewRomanPSMT';"><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">$\Sigma_{</span>p,1}$ <span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">and </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">$\Sigma_{</span>p,2}$ </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">are investigated and sharp results are obtained. Also a new characterization for certain subclass of $\Sigma_<span style="font-size: 8.000000pt; font-family: 'TimesNewRomanPSMT';">p$</span></span> <span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">is proved. </span></p></div></div></div></div></div></div> ER -