Coupled fixed point theorems in quasimetric spaces without mixed monotonicity

In this paper, using the concepts of f-closed set and inverse f-closed set, we will prove some fixed point theorems for graphic contractions in complete quasimetric space. Then, as applications, coupled fixed point theorems in quasimetric spaces without the mixed monotonicity property are obtained.

On exact triangle inequalities in (q1, q2)-quasimetric spaces

For arbitrary (q1, q2) -quasimetric space, it is proved that there exists a function f, such that f -triangle inequality is more exact than any (q1, q2) -triangle inequality. It is shown that this function f is the least one in the set of all concave continuous functions g for which g -triangle inequality hold.

Stability of Functional Equations in Dislocated Quasi-Metric Spaces

We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.

Endpoints inT0-Quasimetric Spaces: Part II

We continue our work on endpoints and startpoints inT0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valuedT0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and theq-hyperconvex hull of its naturalT0-quasimetric space.

Some Fixed Point Theorem for Expansive Type Mapping in Dislocated Metric Space

The purpose of this paper is to present some fixed point theorem in dislocated quasimetric space for expansive type mappings.

q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems

In a previous work, we started investigating the concept of hyperconvexity in quasipseudometric spaces which we calledq-hyperconvexity or Isbell-convexity. In this paper, we continue our studies of this concept, generalizing further known results about hyperconvexity from the metric setting to our theory. In particular, in the present paper, we consider subspaces ofq-hyperconvex spaces and also present some fixed point theorems for nonexpansive self-maps on a boundedq-hyperconvex quasipseudometric space. In analogy with a metric result, we show among other things that a set-valued mappingT∗on aq-hyperconvexT0-quasimetric space (X, d) which takes values in the space of nonempty externallyq-hyperconvex subsets of (X, d) always has a single-valued selectionTwhich satisfiesd(T(x),T(y))≤dH(T∗(x),T∗(y))wheneverx,y∈X. (Here,dHdenotes the usual (extended) Hausdorff quasipseudometric determined bydon the set𝒫0(X)of nonempty subsets ofX.)

Some Properties of Fuzzy Quasimetric Spaces

Some properties of fuzzy quasimetric spaces are studied. We prove that the topology induced by any -complete fuzzy-quasi-space is a -complete quasimetric space. We also prove Baire's theorem, uniform limit theorem, and second countability result for fuzzy quasi-metric spaces.