Abstract
In the present paper, by making use of certain operators of generalized fractional calculus, we introduce a novel class ${\cal T}_{\lambda}^{\mu , \varphi , \eta} (n; \alpha )$ of functions which are analytic and univalent in the open unit disk ${\cal U}.$ A necessary and sufficient condition for a function to be in the class ${\cal T}_{\lambda}^{\mu , \varphi , \eta}(n; \alpha )$ is obtained. In addition, this paper includes distortion theorems involving generalized fractional integrals (and generalized fractional derivatives), radii of close-to-convexity, starlikeness, and convexity. Relevance with some new (or known) special cases are also pointed out.
Citation
H¨useyin Irmak. R. K. Raina. "SOME APPLICATIONS OF GENERALIZED FRACTIONAL CALCULUS OPERATORS TO A NOVEL CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS." Taiwanese J. Math. 8 (3) 443 - 452, 2004. https://doi.org/10.11650/twjm/1500407664
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