Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces. (English) Zbl 0849.47027

Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 2197-2222 (1996).
Summary: This is a survey paper concerning recent developments in the theory of compactness methods for the solvability of nonlinear equations involving accretive operators. We mainly consider mapping results involving various perturbations of accretive operators. The usual methods employed in these results are applications of the Leray-Schauder degree theory as well as various extensions and generalizations of that theory. Several other related results and auxiliary facts are also included, as well as a set of references covering a wide variety of related subjects and problems.
For the entire collection see [Zbl 0836.00032].


47H06 Nonlinear accretive operators, dissipative operators, etc.
47J05 Equations involving nonlinear operators (general)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
47H11 Degree theory for nonlinear operators