Bounds for Probabilities of the Generalized Distribution Defined by Generalized Polylogarithm

Abstract

The paper investigated the polynomials whose coefficients are generalized distribution. Convolution via generalized polylogarithm and subordination methods were employed to obtain the upper bounds for the first few coefficients of the class defined. Furthermore, relevant connections to Fekete-Szego classical theorem were established, particularly in conic region. Conclusively, consequences of various choices of parameters involved were pointed out. The results further established geometric properties of the generalized distribution associated with univalent functions.