Abstract
Abstract In this paper, we introduce a modified version of ordered partial b-metric spaces. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Using this lemma, we prove some fixed point and common fixed point results for ( ψ , φ ) -weakly contractive mappings in the setup of ordered partial b-metric spaces. Finally, examples are presented to verify the effectiveness and applicability of our main results. MSC: 47H10, 54H25.
Highlights
Fixed points theorems in partially ordered metric spaces were firstly obtained in by Ran and Reurings [ ], and by Nieto and Lopez [ ]
The concept of b-metric space was introduced by Bakhtin [ ] and extensively used by Czerwik in [, ]
The following example shows that a convergent sequence {xn} in a partial metric space (X, p) may not be Cauchy
Summary
Fixed points theorems in partially ordered metric spaces were firstly obtained in by Ran and Reurings [ ], and by Nieto and Lopez [ ]. The following example shows that a convergent sequence {xn} in a partial metric space (X, p) may not be Cauchy. Note that in a partial b-metric space the limit of a convergent sequence may not be unique (see [ , Example ]).
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