Some families of <i>p</i>-valent functions with negative coefficients
Titel:
Some families of <i>p</i>-valent functions with negative coefficients
Auteur:
M. K. Aouf
Verschenen in:
Acta mathematica Universitatis Comenianae
Paginering:
Jaargang LXXVIII (2009) nr. 1 pagina's 121-135
Jaar:
2009
Inhoud:
We introduce two subclasses <i>T</i><sup>*</sup>(<i>p</i>, α, <i>j</i>) and <i>C</i>(<i>p</i>, α, <i>j</i>) (0 <FONT SIZE='3' FACE='Symbol'>£</FONT> α <FONT SIZE='3' FACE='Symbol'><</FONT> <i>p</i> – <i>j</i> + 1, 1 <FONT SIZE='3' FACE='Symbol'>£</FONT> <i>j</i><FONT SIZE='3' FACE='Symbol'>£</FONT> <i>p</i>, <br> <i>p</i> <FONT SIZE='3' FACE='Symbol'>Î</FONT> <i>N</i> = {1, 2,...}) of <i>p</i>-valent starlike and <i>p</i>-valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes <i>T</i><sup>*</sup>(<i>p</i>, α, <i>j</i>) and <i>C</i>(<i>p</i>, α, <i>j</i>). We also determine the radii of close-to-convexity and convexity for the functions belonging to the class <i>T</i><sup>*</sup>(<i>p</i>, α, <i>j</i>). Also we obtain several results for the modified Hadamard products of functions belonging to the classes <i>T</i><sup>*</sup>(<i>p</i>, α, <i>j</i>) and <i>C</i>(<i>p</i>, α, <i>j</i>).
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