We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...

We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Kreintype resolvent formulas for Schrödinger operators on bounded Lipschitz domains in R, n > 2. We also discuss the case of bounded C-domains, (1/2) < r < 1.

It is shown that the category of non-Archimedean metric spaces with l-Lipschitz maps can be embedded as a coreflectlve non-bireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and unif’orm properties are derived.

We use basic properties of the projective product, to obtain exponential bounds for the Lipschitz constant associated with the projective product of column{allowable nonnegative matrices. We obtain similar bounds for the associated linear tangent maps.

Our aim in the present paper is three fold. Firstly, we obtain a common fixed point theorem for a pair of self mappings satisfying a Lipschitz type condition employing the property (E.A.) along with a relatively new notion of absorbing pair of maps wherein we never require conditions on the completeness of the space, containment of range of one mapping into the range of other, continuity of the...

We introduce one-sided Lipschitz (OSL) conditions of set-valued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the ...