Fixed point and coupled fixed point theorems on b-metric-like spaces

By M. Alghamdi, Nawab Hussain, Peyman Salimi. Journal of Inequalities and Applications, 2013

159 citations recorded by the source corpus.

We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and uniqueness of fixed points in a b-metric-like space as well as in a partially ordered b-metric-like space. As an application, we derive some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces and b-metric spaces. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results. MSC:47H10, 54H25, 55M20.

Subfields: Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a2379d498d13538a82d4060cf9eb12354c4f7aa1

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Citations in the corpus

Fixed point results for various contractions in parametric and fuzzy b-metric spaces (2015, unknown): “• Let x, y ∈ [2,∞) with x ≤ y, then, 2P(Tx, Ty, t) = 2t(14 + 1 4) 2 = 12 t ≤ t = 1 4 t(1 + 1) 2 ≤ 14 t(x+ y) 2 = 14P(x, y, t) ≤ 14M(x, y, t) = β(P(x, y, t))M(x, y, t) • Let x ∈ [0, 1) and y ∈ [1, 2) (clearly with x ≤ y), then, 2P(Tx, Ty, t) = 2t(18x 2 + 18y) 2 ≤ 2t(18x+ 1 8y) 2 = 1 32 t(x 2 + y2)2 ≤”
An Ulam stability result on quasi-b-metric-like spaces (2016, background): “[10] combined the concepts of b-metric space and metric-like space recently and introduced the so-called b-metric-like spaces.”
Various generalizations of metric spaces and fixed point theorems (2015, background): “For two-variable generalizations of a metric such as metric-like spaces [18], quasi b-metric spaces [132], b-metric-like spaces [14], quasi-metric-like spaces [143], M-metric spaces [22], quaternion-valued metric spaces [12], the relations with metric spaces or with known generalizedmetric spacesmay”