Open AccessA GENERALIZATION OF CERTAIN CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS
Author(s) -
M. K. Aouf,
A. Shamandy
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.26.1995.4384
Subject(s) - mathematics , convexity , distortion (music) , class (philosophy) , product (mathematics) , combinatorics , operator (biology) , generalization , closure (psychology) , convex function , analytic function , regular polygon , discrete mathematics , mathematical analysis , pure mathematics , geometry , physics , artificial intelligence , computer science , market economy , amplifier , biochemistry , chemistry , optoelectronics , cmos , repressor , transcription factor , financial economics , economics , gene
We introduce the subclass $T^*(A,B,n,a)$ ($-1 \le A < B\le 1$, $0 < B \le 1$, $n \ge 0$, and $0\le\alpha <1$) of analytic func;tions with negative coefficients by the operator $D^n$. Coefficient estimates, distortion theorems, closure theorems and radii of close-to-convexety, starlikeness and convexity for the class $T^*(A,B,n,a)$ are determined. We also prove results involving the modified Hadamard product of two functions associated with the class $T^*(A,B,n,a)$. Also we obtain Several interesting distortion theorems for certain fractional operators .of functions in the class $T^*(A,B,n,a)$. Also we obtain class perserving integral operator of the form \[F(z)=\afrc{c+1}{z^c}\int_0^z t^{c-1}f(t) dt, \quad c>-1\]for the class $T^*(A,B,n,a)$. Conversely when $F(z) \in T*(A,B,n,a)$, radius of univalence of $f(z)$ defined by the above equation is obtained.