Abstract
In this paper, it is concerned with the cyclic mapping in b-metric-like spaces. The definition of W -type cyclic mappings is proposed, and then, the existence-uniqueness of the fixed points of these cyclic mappings and the corresponding fixed point theorems are studied. In b-metric-like spaces, the promotion of the concept of cyclic mapping is an interesting topic; then, it is worthy to continue to this part of the promotion. On this basis, the concept of φ -type cyclic mapping is proposed in this article, and the existence-uniqueness of fixed-point problems and the corresponding fixed-point theorem are considered and studied. The results of this paper further generalize and extend some previous results.
Highlights
Let us see how each of the three properties of metric spaces has been investigated
We have explored the development of generalized metric spaces above; for these generalized metric spaces, many mappings in metric spaces and generalization of generalized metric spaces have produced many results
We give the results for φ-type cyclic mapping proposed by us
Summary
Let us see how each of the three properties of metric spaces has been investigated. Let X be a nonempty set and d: X × X ⟶ [0, ∞) be a function such that, for all x, y ∈ X, the following three conditions hold true: (i) d(x, y) ≥ 0, d(x, y) 0⇔x y (ii) d(x, y) d(y, x) (iii) d(x, y) ≤ d(x, z) + d(z, y) en, the pair (X, d) is called a metric space. Let X be a nonempty set and φ: X × X ⟶ R+ be a function such that, for all x, y, z ∈ X, the following three conditions hold true: (i) φ(x, y) 0⇒x y (ii) φ(x, y) φ(y, x) (iii) φ(x, y) ≤ φ(x, z) + φ(z, y) en, the pair (X, φ) is called a metric-like space.
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