Inclusion and neighborhood properties of certain subclasses of $p$-valent analytic functions of complex order involving a linear operator
Bull. Korean Math. Soc. 2014 Vol. 51, No. 6, 1625-1647
https://doi.org/10.4134/BKMS.2014.51.6.1625
Published online November 30, 2014
Ashok Kumar Sahoo and Jagannath Patel
VSS University of Technology, Utkal University
Abstract : By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the $(n,\delta)$-neighborhoods of certain subclasses of $p$-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.
Keywords : $p$-valent analytic functions, complex order, inclusion relationships, Hadamard product, quasi-Hadamard product, subordination, neighborhood
MSC numbers : 30C45
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