Applied general topology 

About: Applied general topology is an academic journal published by Technical University of Valencia. The journal publishes majorly in the area(s): Topological space & Metric space. It has an ISSN identifier of 1576-9402. It is also open access. Over the lifetime, 507 publications have been published receiving 3137 citations. The journal is also known as: @gt. Applied general topology.

On Banach fixed point theorems for partial metric spaces

Abstract: In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in, obtaining as a particular case of our results the Banach fixed point theorem of Matthews ([12]), and some well-known classical fixed point theorems when the partial metric is, in fact, a metric.

A contribution to the study of fuzzy metric spaces

Abstract: We give some examples nad properties of fuzzy metric spaces, in the sense of George and Veramani, and characterize the To topological spaces which admit a compatible uniformity that has a countable transitive base, in terms of the fuzzy theory.

Duality and quasi-normability for complexity spaces

Abstract: The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,) ω . Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provides a suitable setting to carry out an analysis of the dual complexity space. We show that if (E,) is a biBanach space (i.e., a quasi-normed space whose induced quasi-metric is bicomplete), then the function space (B* E , B* ) is biBanach, where B* E = {f : E Σ ∞ n=0 2 -n ( V ) } and B* = Σ ∞ n=0 2 -n We deduce that the dual complexity space admits a structure of quasinormed semlinear space such that the induced quasi-metric space is order-convex, upper weightable and Smyth complete, not only in the case that this dual is a subspace of [0,) ω but also in the general case that it is a subspace of F ω where F is any biBanach normweightable space. We also prove that for a large class of dual complexity (sub)spaces, lower boundedness implies total boundedness. Finally, we investigate completeness of the quasi-metric of uniform convergence and of the Hausdorff quasi-pseudo-metric for the dual complexity space, in the context of function spaces and hyperspaces, respectively.

Best proximity pair theorems for relatively nonexpansive mappings

Abstract: Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → A∪B be a map such that T(A) ⊆ B, T(B) ⊆ A and ǁTx − Tyǁ ≤ ǁx − yǁ, for x in A and y in B. The fixed point equation Tx = x does not possess a solution when A ∩ B = O. In such a situation it is natural to explore to find an element x0 in A satisfying ǁx0 − Tx0ǁ = inf{ǁa − bǁ : a ∈ A, b ∈ B} = dist(A,B). Using Zorn’s lemma, Eldred et.al proved that such a point x0 exists in a uniformly convex Banach space settings under the conditions stated above. In this paper, by using a convergence theorem we attempt to prove the existence of such a point x0 (called best proximity point) without invoking Zorn’s lemma.

Fuzzy quasi-metric spaces

Abstract: We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.