Summary: We present new methods for generating strong stability preserving maps (SSPMs). A first method is based on substitutions of strictly positive real functions with zero relative degree (SPR0 functions) in a Hurwitz polynomial, which consequently generates the family of the concerned operators. For our second method, based on sufficient conditions for the closeness of SPR0 functions by the Hadamard product of a class of polynomials with the numerator and denominator of the SPR0 function, can be interpreted as a vector-matrix product. With the introduction of a non-negative multiplier sequence, we show how the product between the non-negative multiplier sequence and a Hurwitz polynomial can be represented as a SSPM. It is also presented a relationship between stable polynomials and stable polynomials of the Jacobi class by the use of a multiplier sequence of the decreasing kind. In the last section, using generalized products of polynomials, stability and SPR0 functions are preserved by operators that preserve simple rootedness and negative real roots. An extension of families of polynomials depending on parameters is given, and also an extension to operator of deepness-\(k\) on stable polynomials.