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A constructive iterative procedure for solving operator equations. (English. Russian original) Zbl 0833.47053
Comput. Math. Math. Phys. 34, No. 11, 1469-1475 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 11, 1710-1718 (1994).
Summary: An iterative procedure for solving operator equations of general form in Banach spaces by means of which the problem of solving a nonlinear equation reduces to solving equations with almost linear continuous operators, is described. For a wide class of equations in Hilbert space, a constructive iterative procedure which can be used to solve the initial problem is described and the conditions under which it converges to the exact solution are obtained.
47J25 Iterative procedures involving nonlinear operators