A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete archimedean Heyting …eld, a terminal object in the category of archimedean Heyting …elds.

In this paper, we prove existence of coincidence points and a common fixed point theorem for four maps under contractive conditions in cone metric spaces for non continuous mappings and relaxation of completeness in the space. These results extend and improve several well known comparable results in the existing literature. Mathematics Subject Classification: 47H10, 54H25.

Fuzzy logic is a new scientific field which is employed in mathematics, computer science and Engineering. Fuzzy logic calculates the extent to which a proposition is correct and allows computer to manipulate the information. The aim of this paper is to prove some common fixed point theorems using the property E.A. in the setting of G-metric and Fuzzy metric space by taking a set of three condit...

Abstract In this work we define the concepts of coupled orbit and orbitally completeness. After then, using method Bollenbacher Hicks [8], prove some Caristi type fixed point theorems in complete metric spaces for a function P : E × → E. We also give two examples that support our results.

Publicly available benchmark data and metric evaluation approaches have been instrumental in enabling research to advance state of the art methods for remote sensing applications in urban 3D modeling. Most publicly available benchmark datasets have consisted of high resolution airborne imagery and lidar suitable for 3D modeling on a relatively modest scale. To enable research in larger scale 3D...

Let C(X) denote the set of all non-empty closed bounded convex subsets of a normed linear space X. In 1952 Hans R̊adström described how C(X) equipped with the Hausdorff metric could be isometrically embedded in a normed lattice with the order an extension of set inclusion. We call this lattice the R̊adström of X and denote it by R(X). We: (1) outline R̊adström’s construction, (2) examine the struc...

Pterosaurs, a Mesozoic group of flying archosaurs, have become a focal point for debates pertaining to the impact of sampling biases on our reading of the fossil record, as well as the utility of sampling proxies in palaeodiversity reconstructions. The completeness of the pterosaur fossil specimens themselves potentially provides additional information that is not captured in existing sampling ...

Trust is one of the most important factors for participants’ decision-making in Online Social Networks (OSNs). The trust network from a source to a target without any prior interaction contains some important intermediate participants, the trust relations between the participants, and the social context, each of which has an important influence on trust evaluation. Thus, before performing any t...

The notion of wt-distance, introduced by Hussain et al. provides a natural generalization to the b-metric framework well-known and fruitful concept w-distance, initiated Kada Since then, several authors have obtained fixed point theorems for complete spaces with help wt-distances. In this note, we generalize version celebrated Matkowski theorem, stated Czerwik, replacing involved any wt-distanc...