Shape preserving approximation using convex smooth piecewise polynomials for functions in $L_p$ quasi normed spaces

Document Type : Research Paper

Authors

1 Mathematics Department, College of Education for Pure Sciences, University of Babylon, Iraq

2 Mathematics Department, College of Education for pure Sciences, University of Babylon, Babylon, Iraq

Abstract

Many papers used the algebraic polynomials to approximate functions in ${{L}}_{{p}}$ space for $0<p<1$. Few are introduced for the convex algebraic polynomials best approximation. But no one proves direct Theorems for constrained convex approximation using smooth interpolatory piecewise polynomials for functions in ${{L}}_{{p}}$, $0<p<1$. That is what we shall introduce here.

Keywords