In the current paper, we define some subclasses of holomorphic functions in the open disk that are defined by the differential operator. These subclasses are defined in the open disk . We make some estimates for the bounds of the Fekete-Szego inequality as well as the coefficients and for functions that belong to these subclasses. Also, some of the results of these subclasses have been generalized, particularly those that involve the majorization and quasi-subordination concepts.
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