Abstract We prove fractional Sobolev–Poincaré inequalities, capacitary versions of Poincaré and pointwise localized Hardy inequalities in a metric space equipped with doubling measure. Our results generalize extend earlier work where such have been considered the Euclidean spaces or non-fractional setting spaces. The concerning variants are new even case.

We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f+F)~x when / has vanishing strict derivative. In this paper, we present an inverse mapping theorem for set-valued maps F acting from a complete metric space I toa linear space Y with a (translation) invariant metric. We prove that, for any function f: X -> Y with "vanishing strict deri...

The aim of the present paper is to prove a common fixed point theorem for six mappings via pointwise R-weakly commuting mappings in probabilistic metric spaces satisfying contractive type implicit relations. This generalizes several known results in the literature including those of Kumar and Pant (Filomat 22:2 (2008), 43-52), Kumar and Chugh (Sci. Math. Japan. 56 (2002), 269-275) and others. M...

In this paper we show that C-k(X), the set of continuous, realvalued functions on X topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in Rx even when X is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces X for which C-n(X) lies nowhere in the projective hierarchy of the co...

To determine what spaces are the images of “nice” spaces under “nice” mappings is one of the central questions of general topology in 1 . In the past, many noteworthy results on images of metric spaces have been obtained. For a survey in this field, see 2 , for example. A characterization for a quotient compact image of a locally separable metric space is obtained in 3 . Also, such a quotient i...

With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.

I extend the formulation of pseudo-Hermitian quantum mechanics to η(+)-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator η(+). In particular, I give the details of the construction of the physical Hilbert space, observables and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of η(+) and cons...

Abstract In this paper, we study the groups of isometries and set bi‐Lipschitz automorphisms spectral triples from a metric viewpoint, in propinquity framework Latrémolière. particular, prove that these sets are compact automorphism group triple ‐algebra with respect to Monge–Kantorovich metric, which induces topology pointwise convergence. We then necessary sufficient condition for convergence...

Abstract. The present paper discusses the question of formulating and solving minimal-distance problems over the group-manifold of real symplectic matrices. In order to tackle the related optimization problem, the real symplectic group is regarded as a pseudo-Riemannian manifold and a metric is chosen that affords the computation of geodesic arcs in closed forms. Then, the considered minimal-di...

Suppose we are given an infinite, finitely generated group G and a transient random walk with bounded range on the wreath product (Z/2Z) ≀ G, such that its projection on G is transient. This random walk can be interpreted as a lamplighter random walk, where there is a lamp at each element of G, which can be switched on and off, and a lamplighter walks along G and switches lamps randomly on and ...