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Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions

Wanas Abbas Kareem (Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq), abbas.kare.w@qu.edu.iq

In this article, we use the (M,N)-Lucas polynomials to define a new family HΣ(λ,x) of normalized holomorphic and bi-univalent functions and to establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we investigate Fekete-Szegö inequality for functions in the family HΣ(λ,x) which we have introduced here.

Keywords: Holomorphic functions, Univalent functions, Bi-Univalent functions, (M,N)-Lucas polynomials, Upper bounds, Fekete-Szegö inequality, Subordination