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We consider the Darboux problem for the hyperbolic partial functional differential equations (1) Dxyz(X, y) f(x, y, Z(x,y)), (x, y) where Z(x,y) a0, 0] x b0, 0] Z is a function defined by Z(x,y)(t, s) z(x + t, y + s), (t, s) a ao, 0] x bo, 0]. If X I then using the method of functional differential inequalities we prove, under suitable conditions, a theorem on the convergence of the Chaplyghin sequences to the solution of problem (1), (2). In case X is any Banach space we give analogous theoremdoi:10.1155/s1025583499000338 fatcat:6636yl3jnzaoricnrdgu6zeg74