Abstract
Along with the operator equation
, we consider the approximate equations
, which correspond to the following approximation scheme:
For what type of a linear or nonlinear mapping A is it possible to construct a solution u of the equation as a strong limit of solutions u n of the simpler finite-dimensional equations In a series of papers the author studied this problem, and the notion which evolved from these investigations is that of an A-proper mapping. It turned out that the A-properness of A is not only intimately connected with the approximation-solvability of the equation Au = b but, in view of the fact that the class of A-proper mappings is quite extensive, the theory of A-proper mappings extends and unifies earlier results concerning Galerkin type methods for linear and nonlinear operator equations with the more recent results in the theory of strongly monotone and accretive operators, operators of type (S), P γ -compact, ball-condensing and other mappings.
W. V. Petryshyn (1975)
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Zeidler, E. (1990). Inner Approximation Schemes, A-Proper Operators, and the Galerkin Method. In: Nonlinear Functional Analysis and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0981-2_10
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DOI: https://doi.org/10.1007/978-1-4612-0981-2_10
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