Token depositing was established by the method of

successive approximations using a method similar to the procedure described by Malagodi (1967).

Hence, the Gouy phase expression for the exact nondiffracting field solution arises from the Gouy phase expressions for the

successive approximations to the exact HE solution.

Kirk, On

successive approximations for nonexpansive mappings in Banach spaces, Glasgow Math.

The existence proof is made by

successive approximations in [5].

The parameters a, e, s can be determined by the method of

successive approximations at the level of small quantities of order [[epsilon].

The method of

successive approximations is justified for this system in a functional space in which convergence is uniform.

The method of

successive approximations yields the solution of equation (1) [1] as:

Thus, the method of shaping is also known as

successive approximations.

m]} of

successive approximations to a fixed point x of F by the relationship

In paper [6], for the calculation of stress-strain state at normal right-angled sections of bar-shaped structural members, the author proposed a method of

successive approximations (iterative method).

The process of

successive approximations is considered completed when, for ([for all])n, [parallel]{[u.

As described in the earlier work (1) we used the

successive approximations results to the solution of the pendulum's differential equation where the approximation sin([theta])[approximately equal to][theta]-[[theta].