Title: Even and Odd Decompositions of the Bernstein Polynomial Operators

 

 

Abstract: The Bernstein polynomial operator $B_n$ maps a function $f \in C[0,1]$ to a polynomial of  degree at most $n$. Here, the purpose is to investigate the approximation of even or odd  functions in $C[-1,1]$, by constructing operators based upon the Bernstein operators which preserve evenness or oddness. This can be done in more than one way. Two methods will be considered in some detail.