An Application of Legendre Polynomials to Bi-Bazilevic Functions associated with q-Ruscheweyh Operator
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5731Keywords:
Bi-Univalent Functions; Bi-Bazilevic; $q$-Ruscheweyh Differential Operator; Jackson $q$-Derivative Operator, $q$-Gamma Function; Fractional $q$-Calculus Operator; Legendre Polynomials; Coefficient estimates, Fekete-Szeg\"{o} functional problem; Convolution; Hadamard ProductAbstract
In this paper, we make use of the concept of fractional $q$-calculus to introduce a novel class of bi-Bazilevic functions involving $q$-Ruscheweyh differential operator that are subordinate to Legendre Polynomials. This study explores the characteristics and behaviors of these functions, offering estimates for the modulus of the initial Taylor series coefficients $a_{2}$ and $a_{3}$ within this specific class and its various subclasses. Additionally, the research delves into the traditional Fekete-Szeg\"{o} functional problem concerning functions $f$ that are part of our newly defined class and several of its subclasses.
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