A certain subclass of analytic functions associated with operators of fractional calculus
Date
2010-01-08T22:17:11Z
Authors
Raina, R.K.
Srivastava, H.M.
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Abstract
In the present paper we introduce a new class of functions, defined by using certain fractional calculus operators, which are analytic in the open unit disk. A necessary and sufficient condition for a function to belong to such a class is obtained. The various other results presented here include the radii of close-to-convexity, starlikeness, and convexity, and some distortion theorems involving fractional integrals and fractional derivatives. Several special cases of our results are also pointed out.
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Keywords
analytic functions, fractional calculus, Riemann-Liouville operators, Erdelyi-Kober operators, Gauss's hypergeometric function, univalent functions, close-to-convex functions, starlike functions, convex functions