*Correspondence: [email protected] 1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China Full list of author information is available at the end of the article Abstract Based on the concept and properties of C∗-algebras, the paper introduces a concept of C∗-algebra-valued b-metric spaces which generalizes the concept of C∗-algebra-valued metric spac...

In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of R, and we discuss their extension to E. We introduce the notion of E-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of con...

Let (X, d, ) be a partially ordered metric space. Let F, G be two set valued mappings and f , g two single valued mappings on X . We obtained sufficient conditions for existence of common fixed point of F , G, f and g satisfying an implicit relation in X .

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-valued distributions, as well as some extensions of the theory to vector-valued distributions and discrete spaces (weighted graphs). Dedicated to Professor Mathukumalli Vidyasagar on his 70th birthday.

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the uni…cation and re…nement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years ...

In this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero. Let denote the algebra of sets generated by the open ...

On a pseudo-Riemannian manifoldM we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations onM and parallel fields on the metric cone overM for spinor-valued forms.

We introduce one-sided Lipschitz (OSL) conditions of set-valued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the ...

We obtain several Banach-Stone type theorems for vector-valued functions in this paper. Let X,Y be realcompact or metric spaces, E,F locally convex spaces, and φ a bijective linear map from C(X,E) onto C(Y, F ). If φ preserves zero set containments, i.e., z(f) ⊆ z(g)⇐⇒ z(φ(f)) ⊆ z(φ(g)), ∀ f, g ∈ C(X,E), then X is homeomorphic to Y , and φ is a weighted composition operator. The above conclusio...