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We prove a convergence result for a time discrete process of the form $x(t+h)-x\left(t\right)=hV(h,x(t+{\alpha }_1\left(t\right)h),...,x(t+{\alpha }_L\left(t\right)h))t=T+jh,j=0,...,\sigma \left(h\right)-1$ under weak conditions on the function $V$. This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.