East Asian mathematical journal
- Volume 21 Issue 2
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- Pages.219-231
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- 2005
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
SOME RESULTS ASSOCIATED WITH CERTAIN ANALYTIC AND UNIVALENT FUNCTIONS INVOLVING FRACTIONAL DERIVATIVE OPERATORS
- Irmak, H. (Department of Mathematics Education Baskent University Baglica Campus) ;
- Raina, R.K. (Department of Mathematics College of Technology and Engineering M.P. University of Agriculture and Technology)
- Published : 2005.12.31
Abstract
This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.
Keywords
- Normalized analytic functions;
- univalent functions;
- fractional calculus operators;
- convexity;
- starlikeness;
- close-to-convexity;
- quasi-convexity;
- inequalities;
- Jack's Lemma;
- Nunokawa's Lemma