The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

An Approximation of Jordan Decomposable Functions for a Lipschitz Function

Author(s):

Ibraheem Alolyan

Mathematics Department,
College of Science, King Saud University
P.O.Box: 2455, Riyadh 11451,
Saudi Arabia
ialolyan05@yahoo.com


Abstract:

The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a given cellular domain [2,8,9]. In this paper we give an algorithm to approximate such increasing functions when only the values of the function of bounded variation can be computed. For this purpose, we are led to introduce the idea of ε-increasing functions. It is shown that for any Lipschitz continuous function, we can find two ε-increasing functions such that the Lipschitz function can be written as the difference of these functions.

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