Solutions of the Hamilton-Jacobi equation H(x,−Du(x)) = 1, with H(·, p) Hölder continuous and H(x, ·) convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the C-regularity of the extremal trajectories associated with the multifunction generated by DpH .

The objective of this paper is to obtain the properties of αψcompact spaces by using nets, filterbase, αψ-complete accumulation points and so on. We also investigate some properties of αψ-continuous multifunctions and αψ-compact spaces in the context of multifunction.

Let F be a multifunction from a metric space X into L, and B a subset of X . We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F (x) for x ∈ B.

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...

In this paper we analyze, mainly in a finitary setting, the consistency properties of fuzzy possibilities, interpreting them as instances of upper previsions and applying the basic notions of avoiding sure loss and coherence from the theory of imprecise probabilities. It ensues that fuzzy possibilities always avoid sure loss, but satisfy the stronger coherence condition only in a special case. ...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.