Let S be a finite set of n points in d-dimensional space. S is e.(n)-partitionable if there exists a set of d mutually intersecting hyperplanes that divide d-space into 2d open regions, no 2d 1 of which together contain more than o(n) points of S. Willard (1982) has shown that every set in 2-space is :n-partitionable. Yao (1983) has shown that every set in 3-space is gn-partitionable. It is sho...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

a class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. convergence anal...