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

Abstract

This paper presents a new general subfamily NΣmu,v(η,μ,γ,ℓ) of the family Σm 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 am+1 and a2m+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.

Keywords

• holomorphic functions
• univalent functions
• <i>m</i>-fold symmetric bi-univalent functions
• bi-starlike functions
• bi-convex functions
• Ruscheweyh derivative operator