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.