Some Fixed-Point Theorems on Generalized Cyclic Mappings in B-Metric-Like Spaces

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.

Best Approximation Results in Various Frameworks

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial S b -metric spaces. In this way, we obtain extensions of some results in the literature.

Ketunggalan Titik Tetap di Ruang Dislocated Quasi B-Metrik pada Pemetaan Siklik

The quasi b-metric dislocated space (dqb-metric space) was first introduced by Klin-eam and Suanoom in 2015. They had been proven the uniqueness of the fixed point in the dqb-metric space on cyclic mapping that provides the cyclic Banach contraction conditions. Furthermore, in 2016 Dolicanin et al showed that the fixed point singularity properties in the dqb-metric space can be proven without requiring the mapping to satisfy the cyclic metrics Banach contraction conditions. Both statements are proved equivalent in this paper.

Fixed Point Theorems for Cyclic Contractions inC⁎-Algebra-Valuedb-Metric Spaces

We study fundamental properties ofC⁎-algebra-valuedb-metric space which was introduced by Ma and Jiang (2015) and give some fixed point theorems for cyclic mapping with contractive and expansive condition on such space analogous to the results presented in Ma and Jiang, 2015.