‎nanjundan magesh

Our current investigation is primarily motivated by the application of special polynomials in Geometric Function Theory (GFT). This paper aims to utilize (M,N)-Lucas polynomials to estimate the initial coefficient bounds for a subclass of bi-univalent functions consisting of normalized analytic functions. We then derive the famous Fekete-Szegö inequality estimate. We also establish connections between our results and those examined in previous investigations.

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

In this paper, we nd the coefficient bounds by using symmetric Toeplitz determinants for the functions belonging to the subclass R(q).