Abstract
Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.
Highlights
Dis said to be an F metric on X, and the pair (X, D) is called an F-metric space
While M(z, z∗) δr(z∗, Bz∗) δr(z∗, z∗), it shows that r Bz, Sz∗ ≤ Lβr z, z∗ − δr z∗, z∗, (44)
It is obvious that the Lβ-type cyclic mapping is more extensive than a W-type cyclic mapping
Summary
From Definition 1, assume that F denotes the set of continuous function f, and the function f: (0, +∞) ⟶ R which satisfies some conditions is concretely given as follows:. Generalization work of metric spaces is important for fixed point theory. A generation of Banach contraction mapping, which appeared in F-metric spaces, was proposed and some coincident fixed point results were established as follows. Assume that (X, D) is an F-metric space, and let F: X ⟶ X be a given mapping that satisfies the following conditions:. The concept of α − ψ-contraction, which appeared in F-metric spaces [14], was considered; in addition, an interesting and important fixed point result was obtained as follows
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