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𝐋𝐩, Approximation of Functions on Graphs


Abdul Jalil M. Khalaf and Eman Samir Bhaya
Abstract

Lp,G≔Lp Spaces on graphs can be defined naturally, by away analogue to their definitions on intervals. The local properties of these functions in the spaces Lp on the graphs that defined in terms of the vertices of the graph are the same as for the interval case. The global properties depend on the geometric properties of the graph. We introduce a Jackson type theorem for the approximation of functions from Lp,G spaces by polynomials of degree not exceedingn, in terms of the τ- modulus of smoothness of first degree. Our convergence is uniform for any arbitrary graph. We confidence that the result helps to an exceptional understand the Lp spaces on graphs.

Volume 11 | 10-Special Issue

Pages: 767-768

DOI: 10.5373/JARDCS/V11SP10/20192868