About the sequence x kezt we have the following a x 1 EB x b

Last updated: 9/20/2023

About the sequence x kezt we have the following a x 1 EB x b for each 1 to b t b 1 x MKk k 1 te t b t b k20 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x to 6 1 8 B xo b which is given by x t lim x 1 11 b t b b Thus x t lim x ff s x s ds 60 x 60 de lim ff s x s ds x lim f s x s ds Finally the validity of this integral equation has the following two implications 1 x f f s lim x s ds x ff s x s ds E 00 Thus the function 1x 1 satisfying the integral equation x 1 x f f s x s ds for all t t b t b 2 X t x f s x s ds x 0 x dt S dt 0 ff s x s ds f t X t This now proves that the curve X 1 8 4 89 thus obtained is a solution of the initial value problem