Abstract
In this paper, we introduce the notion of 0-σ-complete metric-like space and prove some common fixed point theorems in such spaces. Our results unify and generalize several well-known results in the literature and the recent result of Amini-Harandi [Fixed Point Theory Appl. 2012:204, 2012]. Some examples are included which show that the generalization is proper.
Highlights
Introduction and PreliminariesMatthews [20] introduced the notion of partial metric space as a part of the study of denotational semantics of dataflow network
Matthews showed that the Banach contraction principle is valid in partial metric spaces and can be applied in program verification
We prove common fixed point results in such spaces which generalize the results of Amini-Harandi and several well-known results of metric, partial metric spaces in metric-like spaces
Summary
Introduction and PreliminariesMatthews [20] introduced the notion of partial metric space as a part of the study of denotational semantics of dataflow network. Keywords Common fixed point · Metric-like space · Partial metric space Amini-Harandi [7] generalized the partial metric spaces by introducing the metric-like spaces and proved some fixed point theorems in such spaces. The space (X, p) is said to be 0-complete if every 0-Cauchy sequence in X converges to a point x ∈ X such that p(x, x) = 0.
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