A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

This paper presents a new general subfamily N-Sigma m(u,v) (eta,mu,gamma,l) of the family Sigma(m) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk D associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)|, and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.