An Application of Legendre Polynomials to Bi-Bazilevic Functions associated with q-Ruscheweyh Operator

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, providing estimates for the modulus of the initial Taylor series coefficients a2 and a3 within this specific class and its various subclasses. Additionally, the research delves into the traditional Fekete-Szego<spacing diaeresis> functional problem of functions f belong to the newly defined class and several of its subclasses.