A New Subclass of Meromorfic Starlike Functions Defined by Certain Integral Operator

The aim of this paper is to introduce a new class  \sum \limits _p * ( \alpha , \beta , \sigma) of meromorphically starlike functions defined by certain integral operator in the unit disc  E= { z \mid 0 < |z| <1} and investigate coefficients, distortion properties and radius of convexity for the class. Furthermore, it is shown that the class \sum \limits _p * ( \alpha , \beta , \sigma) is closed under convex linear combinations and integral transforms.

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  • Ch. Pommarenke, On Meromorphic Starlike Functions, Pacific Journal of Mathematics 13 (1963) 221-235.
  • J. Clunie, On Meromorphic Schlicht Functions, Journal of the London Mathematical Society 34 (1959) 215-216.
  • W. C. Royster, Meromorphic Starlike Multivalent Functions, Transactions of the American Mathematical Society 107 (1963) 300-308.
  • I. B. Jung, Y. C. Kim, H. M. Srivastava, The Hardy Space of Analytic Functions Associated with Certain One-Parameter Families of Integral Operators, Journal of Mathematical Analysis and Applications 176 (1993) 138-147.
  • O. P. Juneja, T. R. Reddy, Meromorphic Starlike Univalent Functions with Positive Coefficients, Annales Universitatis Mariae Curie-Sklodowska, sectio A 39 (1985) 65-76.
  • W. G. Atshan, S. R. Kulakarni, Meromorphic p-Valent Functions with Positive Coefficients Defi ned by Convolution and Integral Operator, The Journal of the Indian Academy of Mathematics 29 (2007) 409-423.