ON A SUBCLASS OF MEROMORPHIC FUNCTIONS DEFINED BY HILBERT SPACE OPERATOR

ON A SUBCLASS OF MEROMORPHIC FUNCTIONS DEFINED BY HILBERT SPACE OPERATOR

P. T. Reddy, B. Venkateswarlu, H. Niranjan, R. M. Shilpa

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Abstract

In this paper we introduce and study a new subclass of meromorphic func- tions associated with a certain di erential operator on Hilbert space. For this class, we obtain several properties like the coe cient inequality, growth and distortion theorem, radius of close-to-convexity, starlikeness and meromorphically convexity and integral transforms. Further, it is shown that this class is closed under convex linear combina- tions.

Keywords

Meromorphic functions, Coe cient estimates, Hadamard product, Hilbert space operators.