Metric-like spaces, partial metric spaces and fixed points

Abstract

By a metric-like space, as a generalization of a partial metric space, we mean a pair (X, σ ), where X is a nonempty set and σ : X × X → R satisfies all of the conditions of a metric except that σ (x, x) may be positive for x ∈ X. In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our results unify and generalize some well-known results in the literature. MSC: 47H10

New Geraghty type contractions on metric-like spaces

“…Hitzler and Seda [12] are the first who considered the concept of metric-like (or dislocated metric) spaces. Later, Amini-Harandi [4] established some fixed point results in the class of metric-like spaces. Very recently, many fixed point results on metric-like spaces have been provided.…”

Fixed point theorems for generalized F-contractions in b-metric-like spaces

“…On the other hand, the concept of metric spaces has been generalized by many authors, such as partial metric spaces [18], b-metric spaces [12], metric-like spaces [7], partial b-metric spaces [20], quasi-partial metric spaces [15] and b-dislocated metric spaces [13] were introduced and many results in these spaces were obtained [1,2,8,10,14,16,17]. Recently, the notion of b-metric-like spaces were introduced by Alghamdi [4] and some fixed point theorems were studied in such spaces [4,9].…”

Fixed point results for multivalued mappings on a sequence in a closed ball with applications

“…Dislocated metric space (metric-like space) (see [2,17,25]) is a generalization of partial metric space (see [19,26]). Karapınar et al [17] noticed that the notions metric-like space [2] and dislocated metric space [12] are exactly the same. They also discussed the existence and uniqueness of a fixed point of a cyclic mapping in the context of metric-like spaces.…”