Singular values of two-parameter families λ((b^z − 1)/z)^μ and λ(z/(b^z − 1))^η

Real fixed points and singular values of family of functions arising from generating function of unified generalized Apostol-type polynomials

“…For one parameter families of functions, the real fixed points are studied in [8,9] and the singular values are shown in [10,11]. For two-parameter families, the real fixed points are described in [4,13] and the singular values are found in [13,14]. Generally, the real and complex dynamics of functions are associated to the fixed points and singular values and have become an interesting research area, make worth studying partially due to applicability of these for describing properties of the Julia sets and Fatou sets [1-3, 5, 16].…”

“…For n = 1, the real fixed points and singular values of λ z b z −1 are investigated in [8,9] and [11] respectively. Moreover, it is a generalized family of functions z (e z −1) n [13] on base b and the study of these kinds of maps are scarily found in the literature since most of the work has performed up to now deals with polynomials and rational maps.…”