Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator
munassar, B., Moustafa, A., Sultan, T., EI-Sherbeny, N., Madian, S. (2024). Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator. EKB Journal Management System, 15(2), 1-9. doi: 10.21608/jfca.2024.275040.1074
basheer M munassar; Adela Moustafa; Taha Sultan; Nasser A. EI-Sherbeny; samar M Madian. "Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator". EKB Journal Management System, 15, 2, 2024, 1-9. doi: 10.21608/jfca.2024.275040.1074
munassar, B., Moustafa, A., Sultan, T., EI-Sherbeny, N., Madian, S. (2024). 'Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator', EKB Journal Management System, 15(2), pp. 1-9. doi: 10.21608/jfca.2024.275040.1074
munassar, B., Moustafa, A., Sultan, T., EI-Sherbeny, N., Madian, S. Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator. EKB Journal Management System, 2024; 15(2): 1-9. doi: 10.21608/jfca.2024.275040.1074

Certain Class of Bi-Univalent Functions Associated with Chebyshev Polynomial and q-Difference Operator

Journal of Fractional Calculus and Applications
Volume 15, Issue 2, July 2024, Page 1-9  XML PDF (288.8 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2024.275040.1074
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Authors
basheer M munassar email orcid 1; Adela Moustafaorcid 2; Taha Sultan3; Nasser A. EI-Sherbeny3; samar M Madianorcid 4
1Amran University, Yemen
2Faculty of Science, Mansoura University
3Faculty of Science, Al Azhar University
4Higher Institute of Engineering and Technology New Damietta, Egypt.
Abstract
Using Chebyshev polynomials and q-differential operator, we introduce a novel class of bi-univalent functions within the open unit disk. Initial coefficient bounds for this class are established, emphasizing their significance in complex analysis. Analyticity ensures the representation of these functions through convergent power series, offering a robust tool for comprehending their behavior. The condition of univalence guarantees the one-to-one nature of these functions, preventing multiple mappings of the same point. Researchers employ bi-univalent functions to delve into diverse aspects of complex analysis, unraveling their properties and applications across various mathematical contexts. The exploration encompasses the investigation of geometric properties, including Fekete-Szegö inequality and coefficient bounds, unraveling the intricate interplay between analytic and geometric characteristics. In summary, the study of bi-univalent functions contributes to the depth of complex analysis, providing a nuanced understanding of the relationships between analyticity and univalence. This exploration lays the foundation for advancements in mathematical theory and applications.
Keywords
univalent functions; bi-univalent; starlike and convex functions; coefficient estimates; Fekete-Szegö inequality
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