A Generalized Differential Operator in Function Theory with Applications to Coefficient Bounds of p-Valent Analytic Functions
Abstract
In this paper, a new differential operator that generalizes several well-established operators in geometric function theory by incorporating principles of q-calculus and p-valent analytic functions is introduced. The key objectives include establishing its equivalence to existing operators and deriving coefficient bounds for the associated p-valent function classes. Using q-differentiation and multiplier transformations, we formulate a generalized class of analytic functions and derive coefficient bounds within the unit disk. Numerical comparisons and graphical illustrations reveal that the new operator yields finer results.
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