Abstract
A differential operator is defined on an open unit disk D using the innovative Bell Distribution operator. This operator introduces a new perspective in the study of complex functions within the disk. In this research, the established concept of neighborhoods plays a crucial role. By utilizing these neighborhoods, we aim to derive inclusion relations specifically concerning the (t, n)-neighborhoods of the classes defined by this operator. This approach allows for a deeper understanding of how these classes interact and overlap, providing valuable insights into their structural properties and potential applications in geometric function theory. Through this analysis, we hope to uncover new relationships and behaviors that can enhance our comprehension of differential operators in complex analysis.
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