Comprehensive Subfamilies of Bi-Univalent Functions Defined by Error Function Subordinate to Gegenbauer Polynomials
DOI:
https://doi.org/10.62298/advmath.42Keywords:
Analytic, Univalent, Bi-univalent, Symmetric domain, Error function, Gegenbauer polynomials, Fekete-SzegöAbstract
This work explores coefficient estimates for analytic functions in a symmetric domain. Building on recent studies that use polynomials such as Lucas and Legendre polynomials to bound the Maclaurin coefficients |a2| and |a3|, we turn to Gegenbauer polynomials. By applying the imaginary error function and subordination techniques, we derive sharp bounds for |a2| and |a3| and the Fekete-Szegö functional for two extensive new subclasses. Our general theorems also yield several novel special cases, demonstrating the breadth of our results.
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Copyright (c) 2025 Ali Jan, Minal Khan, Muhammad Shah, Khurshid Ahmad
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