Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators
- 1 September 2007
- journal article
- research article
- Published by Informa UK Limited in Integral Transforms and Special Functions
- Vol. 18 (9), 639-651
- https://doi.org/10.1080/10652460701449668
Abstract
A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk 𝕌. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.Keywords
This publication has 12 references indexed in Scilit:
- Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformationsIntegral Transforms and Special Functions, 2006
- Some functional inequalities and inclusion relationships associated with certain families of integral operatorsComputers & Mathematics with Applications, 2005
- Applications of the Jack lemmaActa Mathematica Hungarica, 2004
- Construction of a Certain Class of Harmonic Close-To-Convex Functions Associated with the Alexander Integral TransformIntegral Transforms and Special Functions, 2003
- Applications of fractional calculus to parabolic starlike and uniformly convex functionsComputers & Mathematics with Applications, 2000
- Some inclusion properties of the classPα(β)Integral Transforms and Special Functions, 1999
- A certain subclass of analytic functions associated with operators of fractional calculusComputers & Mathematics with Applications, 1996
- The Hardy Space of Analytic Functions Associated with Certain One-Parameter Families of Integral OperatorsJournal of Mathematical Analysis and Applications, 1993
- On properties of non-Carathéodory functionsProceedings of the Japan Academy, Series A, Mathematical Sciences, 1992
- A class of distortion theorems involving certain operators of fractional calculusJournal of Mathematical Analysis and Applications, 1988