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.