|
|
 |
| |
|
|
|
A Subclass of Bi-Univalent Functions Associated with the q-Wright Operator |
|
|
|
PP: 459-467 |
|
|
doi:10.18576/amis/200212
|
|
|
|
Author(s) |
|
|
|
Abdullah Alsoboh,
Ala Amourah,
Yousef Al-Qudah,
Amer Darweesh,
Ahmad Al Kasbi,
|
|
|
|
Abstract |
|
|
| Motivated by the growing interaction between $\q$-calculus and geometric function theory, this paper introduces a new subclass of bi-univalent functions defined through a convolution operator associated with the $\q$-Wright function and the $\q$-analogue of Fibonacci numbers. The proposed operator is constructed via the Hadamard convolution, enabling the analytic and combinatorial properties of $\q$-special functions to be naturally embedded into the geometric framework of bi-univalent mappings.
Using the fundamental principal of the subordination, we derive the upper bounds of the initial Taylor--Maclaurin coefficients \( |\varrho_{2}|, |\varrho_{3}| \), and Fekete--Szeg\"{o} inequalities. The analysis further demonstrates how the deformation parameter affects the associated coefficient \( \q \) on the coefficient structure.
The present results highlight the structural significance of \( \q \)-special functions in the construction of convolution-type operators and contribute to the further development of coefficient theory for bi-univalent functions. Moreover, the proposed framework offers a basis for future investigations at the intersection of operator theory and geometric function theory. |
|
|
|
|
|
|
|
