General Topological Vector Spaces Research Articles

Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces

and falls in the scope of fixed point theory for the Hammerstein operators, i.e., operators which can be written KN with K : Z-+ X linear. References to works devoted to this theory can be found in the extensive bibliography given in the survey papers of Dolph and Minty [l] and of Ehrmann [2]. If X and Z are Banach spaces and L-lN is completely continuous on the closure cl Sz of some open bounded set D C X, a very powerful device for proving the existence of fixed points of L-IN is Leray-Schauder degree theory for mappings of the form I T with I the identity and T : cl i2 -+ X completely continuous. Since the publication of the basic and now classical paper of Leray and Schauder [3], their theory has been extended in several ways, A number of them conserve the form of the mapping but allow X to be a more general topological vector space (Rothe [4], Leray [5], Nagumo [6], Browder [7], Altman [8, 93, Klee [lo]), th eir approach remaining in the spirit

On the separation properties of the duals of general topological vector spaces

On the separation properties of the duals of general topological vector spaces