Subclass of meromorphic functions via Hummer Hurwitz Lerch Zeta operators on Hilbert space

Abstract

In this paper, we introduce the Kummer--Hurwitz--Lerch Zeta convolution operator to define a new subclass of meromorphic functions on Hilbert spaces. Using this operator, we construct functions that extend classical meromorphic function theory and derive sharp geometric bounds. We establish coefficient estimates, investigate extreme points, and examine closure properties under convex combinations. Additionally, the radii of meromorphic starlikeness, convexity, and close-to-convexity are determined. The Hadamard product of functions in this subclass is studied, and integral operators are explored to extend the geometric and analytic properties of the class.