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

Pishtiwan Othman Sabir, Hari Mohan Srivastava (), Waggas Galib Atshan, Pshtiwan Othman Mohammed (), Nejmeddine Chorfi and Miguel Vivas-Cortez ()
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Pishtiwan Othman Sabir: Department of Mathematics, College of Science, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Waggas Galib Atshan: Department of Mathematics, College of Science, University of Al-Qadisiyah, Al-Diwaniyah 58001, Al-Qadisiyah, Iraq
Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
Nejmeddine Chorfi: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Miguel Vivas-Cortez: Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de Octubre 1076 y Roca, Quito 170143, Ecuador

Mathematics, 2023, vol. 11, issue 18, 1-13

Abstract: This paper presents a new general subfamily N Σ m u , v ( η , μ , γ , ℓ ) of the family Σ 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 2 m + 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; m -fold symmetric bi-univalent functions; bi-starlike functions; bi-convex functions; Ruscheweyh derivative operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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