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A certain subclass of analytic functions involving operators of fractional calculus
(Pergamon-Elsevier Science Ltd, 1998) Chen, MP; Irmak, H; Srivastava, HM
Making use of certain operators of fractional calculus, we introduce a new class T-mu(n,lambda,alpha) of functions which are analytic and univalent in the open unit disk U and obtain a necessary and sufficient condition for a function to be in the class T-mu(n,lambda,alpha). The various other results presented here for the class T-mu(n,lambda,alpha) include the radii of close-to-convexity, starlikeness, and convexity, end some growth and distortion theorems involving fractional integrals and fractional derivatives. Some interesting consequences and possible further generalizations of these results are also pointed out.
Some families of multivalently analytic functions with negative coefficients
(Academic Press Inc Jnl-Comp Subscriptions, 1997) Chen, MP; Irmak, H; Srivastava, HM
The authors introduce and study three novel subclasses of analytic and p-valent functions with negative coefficients. In addition to finding a necessary and sufficient condition for a function to belong to each of these subclasses, a number of other potentially useful properties and characteristics of functions in these subclasses are obtained. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered. (C) 1997 Academic Press.