Abstract
In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk.
Highlights
The field of geometric function theory is rich with different types of linear, differential, integral, and mixed operators
We present a linear operator formulated by the Airy functions [5], which are special functions determined by the hypergeometric function of a complex variable
By using the new operator, we defined a new class of analytic functions and investigated its properties
Summary
The field of geometric function theory is rich with different types of linear, differential, integral, and mixed operators. We present a linear operator formulated by the Airy functions [5], which are special functions determined by the hypergeometric function of a complex variable. These functions are solutions for the Airy equation f (z) – zf (z) = 0. The class of these differential equations plays an important role in applied sciences such as optics, economy, and astronomy. The formula of the Airy function of a complex variable is given by ζ3
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