Volume 26 , Issue 3 , PP: 242-258, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Waleed Al-Rawashdeh 1 *
Doi: https://doi.org/10.54216/IJNS.260317
This paper introduces two new classes of bi-Bazilevic and bi-univalent functions that are defined using Borel distribution and Ruscheweyh operator, which also associated with Legendre polynomials and modified Sig-moid function within the open unit disk D. This paper explores the characteristics and behaviors of these functions, we find estimates for the modulus of the initial Taylor series coefficients a2 and a3 for functions within our newly defined classes and some of their various subclasses. Moreover, this paper explores the classical Fekete-SzegÖ functional problem concerning functions f that are classified within our specific classes. Additionally, we obtain the classical Fekete-SzegÖ inequalities of functions belonging to these classes and some of their various subclasses.
Bi-Univalent Functions , Bi-Bazilevic , Borel Distribution , Ruscheweyh operator , Modified Sig-moid Function , Legendre Polynomials , Coefficient estimates , Fekete-Szeg¨ , o functional problem , Convolution , Hadamard Product
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