Abstract
In this paper, we define a new operator on the class of meromorphic functions and define a subclass using Hilbert space operator. Coefficient estimate, distortion bounds, extreme points, radii of starlikeness, and convexity are obtained.
Highlights
Let Σ denote the class of meromorphic functions f (z)
For f ∈ Σ given by (1) and g ∈ Σ given by g (z)
For a complex-valued function f analytic in a domain E of the complex plane containing the spectrum σ(T) of the bounded linear operator T, let f(T) denote the operator on H defined by the RieszDunford integral [4]
Summary
For a complex-valued function f analytic in a domain E of the complex plane containing the spectrum σ(T) of the bounded linear operator T, let f(T) denote the operator on H defined by the RieszDunford integral [4]. We introduce a subclass MP(α, λ, T) of Σ defined using Hilbert space operator and prove a necessary and sufficient condition for the function to belong to this class, the distortion theorem, radius of starlikeness, and convexity. In [6], Atshan and Buti had defined an operator acting on analytic functions in terms of a definite integral. We modify their operator for meromorphic functions as follows. For all operators T with ‖T‖ < 1 and T ≠ 0, 0 being the zero operator on H
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