In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

We establish improved mean value estimates associated with the number of integer solutions certain systems diagonal equations, in some instances attaining sharpest conjectured conclusions. This is first occasion on which bounds this quali

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

we consider   bivariate  mean-value interpolationproblem, where the integrals over circles are interpolation data. in this case the problem  is described  over   circles of the same radius and with  centers are on astraight line and it is shown that in this case the interpolation is not correct.