We consider a fractional version of Gauß capillarity energy. A suitable extension problem is introduced to derive boundary monotonicity formula for local minimizers this As consequence, blow-up limits are shown subsequentially converge minimizing cones. Finally, we show that in the planar case there only one possible cone, determined by Young’s law.

In this paper, we introduce the concept of IVF weakly M -continuity and investigate some characterizations for IVF weakly M -continuous mappings between an IVF minimal space and an IVF topological space.

A function f :R → {0, 1} is weakly symmetric (weakly symmetrically continuous) at x ∈ R provided there is a sequence hn → 0 such AMS classification numbers: Primary 26A15; Secondary 03E50, 03E35.

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...

A weak form of weak quasi-continuity, which we call subweak quasi-continuity, is introduced. It is shown that subweak quasi-continuity is strictly weaker than weak quasicontinuity. Subweak quasi-continuity is used to strengthen several results in the literature concerning weak quasi-continuity. Specifically, results concerning the graph, graph function, and restriction of a weakly quasi-continu...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

Abstract. In this paper, the authors defined a multifunction F : X → Y to be upper (resp. lower) weakly α-continuous if for each x ∈ X and each open set V of Y such that F (x) ⊂ V (resp. F (x) ∩ V 6= ∅), there exists an α-open set U of X containing x such that U ⊂ F(Cl(V )) (resp. U ⊂ F−(Cl(V ))). They give some characterizations and several properties concerning upper (lower) weakly α-continuo...

Let A and B be two Banach algebras and let M be a Banach B-bimodule. Suppose that σ : A → B is a linear mapping and d : A → M is a σ-derivation. We prove several results about automatic continuity of σderivations on Banach algebras. In addition, we define a notion for m-weakly continuous linear mapping and show that, under certain conditions, d and σ are m-weakly continuous. Moreover, we prove ...

Bridges 1992 has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers wi...

This paper presents new fixed point results for weakly sequentially upper semicontinuous maps defined on locally convex Hausdorff topological spaces which are angelic when furnished with the weak topology. Moreover, we establish an applicable Leray-Schauder alternative (Theorem 2.12) for a certain subclass of these maps. Our alternative combines the advantages of the strong topology (i.e., the ...