a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

In this paper, we propose a new iteration process to approximate minimizers of proper convex and lower semi-continuous functions and fixed points of λ-hybrid multivalued mappings in Hilbert spaces. We also provide an example to illustrate the convergence behavior of the proposed iteration process and numerically compare the convergence of the proposed iteration scheme with the existing schemes.

Motivated by the theory of kinetic models in gas dynamics, we obtain an integral representation of lower semi-continuous functions on Rd, d ≥ 1. We use the representation to study the problem of compactness of a family of the solutions of the discrete time BGK model for the compressible Euler equations.

Theory The abstract theory of large deviations was first formulated in 1966 by the Indian American mathematician Srinivasa Varadhan (see [Var]), who was awarded the prestigious Abel prize for 2007 “for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations”. The American mathematician Monroe David Donsker also made a significant c...

Let X, d be a metric space and S a closed and nonempty subset of X. Denote by 2 resp., C X the family of all nonempty resp., nonempty and closed subsets of X. A mapping T : S → 2 is said to satisfy condition P if, for every closed ball B of S with radius r ≥ 0 and any sequence {xn} in S for which d xn, B → 0 and d xn, T xn → 0 as n → ∞, there exists x0 ∈ B such that x0 ∈ T x0 where d x, B inf{d...

The aim of this paper is to introduce semi strong na continuous multifunctions and to obtain new results.

Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.