ABSTRACT
This chapter describes some connections between approximation processes and evolution problems and, in particular, the possibility of approximating the solutions of more general diffusion models using a generalization of the binomial coefficients in some classical approximation processes. This enlarged class of evolution problems includes some diffusion models of particular interest as gene frequency models in population genetics, when selection, migration, mutation and other factors occur. In the interval [0,1], the approximation processes taken into consideration are of Bernstein-type for continuous functions and of Bernstein-Kantorovitch-type for L p -integrable functions; on the half-line, we consider Bernstein-Chlodovski-type operators and Baskakov-type operators; finally, we shall be also concerned with Bernstein-type operators on the hypercube and on the standard simplex of R d .
