Very recently, N. Souayan and N. Mlaiki [Nazir Souayan and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-139] and S. Sedghi et al. [S. Sedghi, A. Gholidahneb, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in Sb-metric spaces, to appear in J. Linear Topol. Algebra], introduced the concept of Sb-metric space as a generalization of S-metric space. In this paper, we modified the definition of Sb-metric introduced by Souayan and Mlaiki and prove some coupled common fixed point theorems in Sb-metric space. We also present an example to confirm our theoretical results.

In this manuscript, we prove some common fixed point theorems for occasionally weakly compatible mappings in fuzzy cone metric space.

In this paper, we discuss about various generalizations of α − admissible mappings. Furthermore, we extend the concept of α − admissible to generalize rational α − Geraghty contraction in G − metric space. With this new contraction mapping, we establish some fixed-point theorems in G − metric space. The obtained result is verified with an example.

In this paper we prove the existence and uniqueness of couple fixed point theorems for three mappings satisfying some new rational contractive conditions. We prove our results in the frame work of Gb-metric space which is recently introduced by Aghajani et al. (Filomat 28(6):1087–1101, 2014). Illustrative example is also given to support our result.

This study aims to provide some new classes of (α,β,F*)-weak Geraghty contraction and (α,β,F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem.

In this paper, we prove the existence of best proximity points of cyclic contractions and generalised proximal rational contractions of first and second kind in the setting of complete b-metric space. Some results are also given in the form of corollaries.

In this note we obtained a new related fixed point theorem on three metric spaces of which one is compact. Here we consider three mappings, not all of which are necessarily continuous. Our result generalizes some earlier results.

Abstract In this paper, we introduce a new type of contraction to seek the existence of tripled best proximity point results. Here, using the new contraction and P-property, we generalize and extend results of W. Shatanawi and A. Pitea and prove the existence and uniqueness of some tripled best proximity point results. Examples are also given to support our results.