APPROXIMATION OF NONLINEAR OPERATOR EQUATIONS^*

Abstract

Some stationary and nonstationary projection-iteration methods for a wide class of nonlinear operators are studied. Strong and weak convergence theorems are established. A generalized Edelstein's fixed point theorem is stated. By means of this theorem and of the studied methods one can solve approximately a number of nonlinear operator equations for which the usual Picard method is not applicable.

^*This paper was supported by the National Fundamental Research Program in Natural Science of Vietnam.

Keywords:

• Nonlinear operator
• Implicit method
• Stationary
• Nonstationary
• Generalized Edelstein's fixed point theorem
• AMS Subject Classifications: 46N40; 65Jxx

Acknowledgments

Notes

^*This paper was supported by the National Fundamental Research Program in Natural Science of Vietnam.