Abstract
The aim of this paper is to define modified weakα-ψ-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangularα-admissibility. As an application, we prove new fixed point results for graphic weakψ-contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.
Highlights
Introduction and PreliminariesThe concept of partial metric space was introduced by Matthews [1] in 1994
Several authors studied the problem of existence and uniqueness of a fixed point for mappings satisfying different contractive conditions on partial metric spaces (e.g., [4,5,6,7,8,9,10])
Fixed Point Results in Partially Ordered Partial Metric Spaces
Summary
The concept of partial metric space was introduced by Matthews [1] in 1994. Partial metric space is a generalized metric space in which each object does not necessarily have to have a zero distance from itself. A partial metric space (X, p) is said to be complete if every Cauchy sequence {xn} in X converges, with respect to τp, to a point x ∈ X such that p(x, x) = limn,m → ∞p(xn, xm). A partial metric space (X, p) is said to be 0-complete if every 0-Cauchy sequence {xn} in X converges, with respect to τp, to a point x ∈ X such that p(x, x) = 0. Let (X, d) be a complete metric space and T be α-admissible mapping. Let (X, d) be a complete metric space and T be α-admissible mapping with respect to η. We define modified weak α-ψ-contractive mappings and establish fixed point results for such mappings defined on ordinary as well as ordered partial metric spaces using the notion of triangular α-admissibility. Some examples and an application to integral equation are given here to illustrate the usability of the obtained results
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