A modification to L_{p,\alpha} and its applicability in error estimation of triangular functions

Error estimate and rate of convergence are two important topics in the field of numerical analysis. A convenient normed space corresponding to the problem under regard can have better upper bounds. This paper introduces a weighted normed space L_{p,\omega} which from the measure theory point of view, is a special case of L^{p} space. This space is a modification of L_{p,\alpha} space, which is introduced before in \cite{Baghani}. Next, by using L_{p,\alpha}-norm, we compute a two-variable upper bound of the triangular function.

Keywords:

L_{p , \alpha} space , L_{p , \omega} space , Error estimation , Triangular functions