Generalized classes of starlike and convex functions of order α

We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have a...

Full description

Saved in:
Bibliographic Details
Main Authors: Shigeyoshi Owa, C. Y. Shen
Format: Article
Language:English
Published: Wiley 1985-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171285000503
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832552881765482496
author Shigeyoshi Owa
C. Y. Shen
author_facet Shigeyoshi Owa
C. Y. Shen
author_sort Shigeyoshi Owa
collection DOAJ
description We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.
format Article
id doaj-art-d3e46958a1e14daebe3778426bb37e7b
institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1985-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-d3e46958a1e14daebe3778426bb37e7b2025-02-03T05:57:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018345546710.1155/S0161171285000503Generalized classes of starlike and convex functions of order αShigeyoshi Owa0C. Y. Shen1Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577, JapanDepartment of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C. V5A 1S6, CanadaWe have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.http://dx.doi.org/10.1155/S0161171285000503subordinationfractional derivativefractional integralgeneralized Libera operator.
spellingShingle Shigeyoshi Owa
C. Y. Shen
Generalized classes of starlike and convex functions of order α
International Journal of Mathematics and Mathematical Sciences
subordination
fractional derivative
fractional integral
generalized Libera operator.
title Generalized classes of starlike and convex functions of order α
title_full Generalized classes of starlike and convex functions of order α
title_fullStr Generalized classes of starlike and convex functions of order α
title_full_unstemmed Generalized classes of starlike and convex functions of order α
title_short Generalized classes of starlike and convex functions of order α
title_sort generalized classes of starlike and convex functions of order α
topic subordination
fractional derivative
fractional integral
generalized Libera operator.
url http://dx.doi.org/10.1155/S0161171285000503
work_keys_str_mv AT shigeyoshiowa generalizedclassesofstarlikeandconvexfunctionsofordera
AT cyshen generalizedclassesofstarlikeandconvexfunctionsofordera