We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and uniqueness of fixed points in a b-metric-like space as well as in a partially ordered b-metric-like space. As an application, we derive some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces and b-metric spaces. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results. MSC: Primary 47H10; 54H25; 55M20

The aim of this work is to modify the notions of α-admissible and α-ψ-contractive mappings and establish new fixed point theorems for such mappings in complete metric spaces. Presented theorems provide main results of Karapinar and Samet (Abstr. Appl. Anal. 2012Anal. :793486, 2012 and Samet et al. (Nonlinear Anal. 75:2154-2165 as direct corollaries. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

In this paper, we introduce the notion of α-ψ-Meir-Keeler contractive mappings via a triangular α-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results. MSC: 46N40; 47H10; 54H25; 46T99

In this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings.