Open AccessON SPIRALLIKE INTEGRAL OPERATORS
Author(s) -
Subhas S. Bhusnoormath,
Manjunath V. Devadas
Publication year - 1994
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.25.1994.4445
Subject(s) - lambda , mathematics , beta (programming language) , alpha (finance) , class (philosophy) , combinatorics , pure mathematics , physics , statistics , computer science , quantum mechanics , construct validity , artificial intelligence , programming language , psychometrics
In this paper the integral operators \[ F(z)=\left[\frac{\beta+\gamma}{z^\gamma}\int_0^z [f(t)]^\beta t^{\gamma-1} dt\right]^{1/\beta}\]for $f(z) \in S^\alpha(\lambda, a, b)$ are studied. $S^\alpha(\lambda, a, b)$ as a subclass of the class of all spirallike functions was introduced and studied by the authors. It is shown that $F(z)$ is also in $S^\alpha(\lambda, a, b)$, whenever $f(z)$ is in $S^\alpha(\lambda, a, b)$, under certain restrictions.