Semi-numerical Approximation Structures for Nonlinear Noncompact Operators in Banach Spaces

Abstract

The A-proper operators, introduced by F. E. Browder and W. V. Petryshyn (Browder, F. E., Petryshyn, W. V. (1968). The topological degree and Galerkin approximations for noncompact operators in Banach spaces. Bull. Amer. Math. Soc. 74:641–646; Browder, F. E., Petryshyn, W. V. (1969). Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces. J. Funct. Anal. 3:217–245.), arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. In the last years, much attention has been paid to the study of linear semi-numerical approximation schemes of Galerkin type. In this article the uniform limits, sums, and compositions of A-proper maps are investigated, as well as their generalized topological degree with respect to various nonlinear approximation schemes.

Keywords:

• Approximation scheme
• A-Proper operator
• AMS Subject Classification: 47H09
• 47H11