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A modification of the convergence conditions for Picard's iteration

The convergence of the method of successive approximations is usually studied by the fixed point theorem. An alternative to this theorem is given in this work, where a contraction mapping is not necessary. An application to nonlinear integral equations of Fredholm type and second kind is also presented.

nonlinear equations in Banach spaces; Picard's iteration; semilocal convergence


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