Class-mapping properties of the Hohlov operator
Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 51-65
Printed January 1, 2011
Akshaya K. Mishra and Trailokya Panigrahi
Berhampur University, Knowledge Campus
Abstract : In the present paper sufficient conditions, in terms of hypergeometric inequalities, are found so that the Hohlov operator preserves a certain subclass of close-to-convex functions (denoted by ${\mathcal {R}}^\tau(A,B)$) and transforms the classes consisting of $k$-uniformly convex functions, $k$-starlike functions and univalent starlike functions into ${\mathcal {R}}^\tau(A,B)$.
Keywords : univalent, $k$-uniformly convex, parabolic starlike, hypergeometric series, Hadamard product, Hohlov operator
MSC numbers : 30C45, 33E05
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