Geometric Properties of a Novel Subclass of Meromorphic Multivalent Functions Defined by a Linear Operator
Keywords:
Meromorphic functions, multivalent functions, linear operator, geometric function theoryAbstract
The field of geometric function theory is significantly enriched by the study of meromorphic functions, particularly those that are multivalent. Operators play a crucial role in defining and investigating novel subclasses of these functions, allowing for a deeper understanding of their geometric properties such as starlikeness, convexity, and close-to-convexity. This paper introduces and rigorously examines a new subclass of meromorphic multivalent functions by employing a generalized linear operator. Building upon established principles of differential subordination and superordination, as well as fractional calculus, we derive several key characteristics of functions belonging to this subclass, including coefficient bounds, inclusion relationships with other known function classes, and conditions for multivalent starlikeness and convexity. The results presented here extend previous work in the area and provide new insights into the complex analytical behavior of these functions. These findings contribute to the broader understanding of mathematical operators' applications in complex analysis and offer a foundation for further research into related function spaces and their potential applications.
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Copyright (c) 2025 Prof. Marco Ricci, PhD, Dr. Sophie Dubois
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