| Paper title: |
A Note on Starlike Functions of Order α Associated with a Fractional Calculus Operator Involving Caputo |
| Published in: | Issue 1, (Vol. 5) / 2011 |
| Publishing date: | 2010-04-29 |
| Pages: | 97-101 |
| Author(s): | SALAH Jamal, DARUS Maslina |
| Abstract. | In this article, we introduce a class of starlike functions of order α by using a fractional operator involving Caputo's fractional which was introduced recently by the authors. The coefficient inequalities and distortion theorems are determined. Further some subordination theorems are given. In addition, results involving Hadamard product are also discussed. |
| Keywords: | Caputo's Differentiation Operator; Hadamard Product; Distortion Theorem. |
| References: | 1. S. Owa, Generalized Classes Of Starlike and Convex Functions of order , J.Math. Math. Sci. Vol. 8 No. 3 (1985) 455-467. 2. T. Sekine, Generalization Of Certain Subclasses Of Analytic Functions, J. Math. Sci. Vol. 10 No. 4 (1987) 725-732. 3. R.Bharati, R. Parvatham and A.Swaminathan, On subclass of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 28(1) (1997), 17-33. 4. H.Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51(1975), 109-116. 5. J. Salah and M. Darus, A subclass of uniformly convex functions associated with a fractional calculus operator involving Caputo's fractional differentiation. Acta Universitatis Apulensis. No. 24/2010, 295-304. 6. S.S. Miller, P.T. Mocanu and M.O. Reade, Subordination preserving integral operators, Babes- Bolyai Univ.Fac.Math.Res.Semin. 4 (1983), 42-56. |
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