Fractional Calculus Operator and Certain Applications in Geometric Function Theory
DOI:
https://doi.org/10.5644/SJM.06.1.04Keywords:
Open unit disk, analytic, multivalent, starlike, convex, closeto-convex functions, fractional calculus, Jack’s LemmaAbstract
Using a operator involving fractional calculus introduced by Owa and Srivastava [8], two novel families: $${\mathcal V}_{\delta}^{\alpha, \beta}(\nu;\gamma)\;\; \mbox{and} \;\;{\mathcal W}_{\delta}^{\alpha, \beta}(\mu;\gamma)$$ $$(\delta\neq 0,\; \alpha <1,\;\beta <1,\;\gamma <1,\;\mu\geq 0,\;\nu\in (-1,0)\cup(0,1))$$ of functions $f(z)$ which are analytic and univalent in the open unit disk ${\mathcal U}$ are defined. Moreover some consequences of main results are shown.
2000 Mathematics Subject Classification. 30C45, 30A10, 26A33
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References
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