Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated -ideals are studied. These -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.
We give in this paper conditions for a mapping to be globally injective in a topological vector space.
It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator can be approximated by a sequence of maximal monotone operators of type NI, which converge to in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class as a generalization of and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.
We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in . The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.
The aim of this paper is to obtain monotonic solutions of an integral equation of Urysohn-Stieltjes type in . Existence will be established with the aid of the measure of noncompactness.
This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...