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.
Baghani, O., & Azin, H. (2023). A modification to $L_{p,\alpha}$ and its applicability in error estimation of triangular functions. Journal of Frame and Matrix Theory, 1(1), 9-14. doi: 10.22034/jfmt.2023.421933.1008
MLA
omid Baghani; Hadis Azin. "A modification to $L_{p,\alpha}$ and its applicability in error estimation of triangular functions". Journal of Frame and Matrix Theory, 1, 1, 2023, 9-14. doi: 10.22034/jfmt.2023.421933.1008
HARVARD
Baghani, O., Azin, H. (2023). 'A modification to $L_{p,\alpha}$ and its applicability in error estimation of triangular functions', Journal of Frame and Matrix Theory, 1(1), pp. 9-14. doi: 10.22034/jfmt.2023.421933.1008
VANCOUVER
Baghani, O., Azin, H. A modification to $L_{p,\alpha}$ and its applicability in error estimation of triangular functions. Journal of Frame and Matrix Theory, 2023; 1(1): 9-14. doi: 10.22034/jfmt.2023.421933.1008
)