Applications of (M,N)-Lucas Polynomials for a Certain Family of Bi-Univalent Functions Associating λ-Pseudo-Starlike Functions with Sakaguchi Type Functions

Abbas Kareem Wanas; Elham Kareem Wanas; Adriana  Cătaş; Mohamed  Abdalla

doi:10.34198/ejms.15125.001010

Abbas Kareem Wanas Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq
Elham Kareem Wanas College of Engineering, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq
Adriana Cătaş Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania
Mohamed Abdalla Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia

DOI: https://doi.org/10.34198/ejms.15125.001010

Keywords: bi-univalent function, λ-pseudo-starlike function, Sakaguchi type function, (M,N)-Lucas polynomials, coefficient bounds, Fekete-Szegö problem

Abstract

In this article, we use the (M,N)-Lucas Polynomials to determinate upper bounds for the Taylor-Maclaurin coefficients $\left|a_{2}\right|$ and $\left| a_{3}\right|$ for functions belongs to a certain family of holomorphic and bi-univalent functions associating $\lambda$-pseudo-starlike functions with Sakaguchi type functions defined in the open unit disk $\mathbb{D}$. Also, we discuss Fekete-Szeg\"{o} problem for functions belongs to this family.

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Applications of (M,N)-Lucas Polynomials for a Certain Family of Bi-Univalent Functions Associating λ-Pseudo-Starlike Functions with Sakaguchi Type Functions

Abstract

References

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