Abstract
ObjectivesWe explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized ({check{psi }}, hat{eta })-weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings.ResultIn partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.
Highlights
In a wide range of pure and applied mathematics problems, fixed points of mappings that satisfy contractive conditions in extended metric spaces are extremely useful
Ran and Reuings [32] described the existence of fixed points in this direction for certain maps in ordered metric space and exhibited matrix linear equations applications
Lakshmikantham and Ćirić [22], which were the extensions of [11] involving monotone property to a function in the space, pioneered the idea of coupled coincidence, common fixed point results. [19, 25, 34–37] provide additional information on coupled fixed point effects in various spaces under various contractive conditions
Summary
In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.
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