We study continuity envelopes in spaces of generalized smoothness B ,N p,q (R n) and F σ ,N p,q (R n). The results are applied in proving sharp embedding assertions in some limiting situations. © 2008 Elsevier Inc. All rights reserved.

and Applied Analysis 3 0 in any metric linear spaces. Let X,Λ,M, Y be metric linear spaces. Let Y ∗ be the topological dual space of Y . Let C ⊂ Y be a pointed, closed, and convex cone with intC/ ∅, where intC denotes the interior of C. Let C∗ : {f ∈ Y ∗ : f y ≥ 0, for all y ∈ C} be the dual cone of C. Since intC/ ∅, the dual cone C∗ of C has a weak∗ compact base. Letting e ∈ intC be given, the...

In this paper, by using a weaker assumption, we discuss the Hölder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set-valued one, but not a single-valued one. These results extend the recent ones in the literature. Several examples are given for the illustration of our results.

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α (0 < α < 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of mod...

We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness B p,q (Rn) into generalized Hölder spaces Λ μ(·) ∞,r(R) when s(Nτ−1) > 0 and τ−1 ∈ `q′ , where τ = σN−n/p. A borderline situation, corresponding to the limiting situation in the classical case, is included and give new results. In particular, we characterize optimal embeddings for B-spaces. As ...

This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a ge...

In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonli...

We study a generalized notion of topology which evolved from applications in the area of logic programming semantics. The generalization is obtained by relaxing the requirement that a neighbourhood of a point includes the point itself, and by allowing neighbourhoods of points to be empty. We show that it is meaningful to discuss neighbourhoods, convergence, and continuity in these spaces. A gen...

We study a generalized notion of topology which evolved from applications in the area of logic programming semantics The generalization is obtained by relaxing the requirement that a neighbourhood of a point includes the point itself and by allowing neighbourhoods of points to be empty We show that it is meaningful to discuss neighbourhoods convergence and continuity in these spaces A generaliz...

We study generalized fractional p-Laplacian equations to prove local boundedness and Hölder continuity of weak solutions such nonlocal problems by finding a suitable Sobolev-Poincaré inquality.