Abstract
We introduce a generalization of the Meir‐Keeler‐type contractions, referred to as generalized Meir‐Keeler‐type contractions, over partial metric spaces. Moreover, we show that every orbitally continuous generalized Meir‐Keeler‐type contraction has a fixed point on a 0‐complete partial metric space.
Highlights
In 1992, Matthews introduced the notion of a partial metric space which is a generalization of usual metric space 1
We introduce a generalized Meir-Keeler-type contraction on partial metric spaces
We show an orbitally continuous self-mapping T on a 0-complete partial metric spaces satisfying that generalized Meir-Keeler-type contraction has a unique fixed point
Summary
In 1992, Matthews introduced the notion of a partial metric space which is a generalization of usual metric space 1. The following example shows that there exists a 0-complete partial metric which is not complete. A self-mapping F on a partial metric space X, p is continuous at x ∈ X if and only if for every ε > 0, there exists δ > 0 such that F Bp x, δ ⊆ Bp Fx, ε see, e.g., 15 .
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