In this paper, we introduce the concept of a Hausdorff dislocated metric. We initiate the study of fixed point theory for multi-valued mappings on dislocated metric space using the Hausdorff dislocated metric and we prove a generalization of the well known Nadler's fixed point theorem. Moreover, we provide some examples and we give an application of our main result.

In this paper, we introduce some generalized nonlinear contractions via implicit functions and α-admissible pair of mappings. We also provide some common fixed point results for above contractions in the class of b-metric-like spaces. We will derive some consequences and corollaries from our obtained results. Some illustrated examples are presented to make effective the concepts and results.

In this paper, using the concept of α-admissible pairs of mappings, we prove several common fixed point results in the setting of b-metric-like spaces. We also introduce the notion of generalized cyclic contraction pairs and establish some common fixed results for such pairs in b-metric-like spaces. Some examples are presented making effective the new concepts and results. Moreover, as consequences we prove some common fixed point results for generalized contraction pairs in partially ordered b-metric-like spaces.

Based on concepts of α-admissible mappings and simulation functions, we establish some fixed point results in the setting of metric-like spaces. We show that many known results in the literature are simple consequences of our obtained results. We also provide some concrete examples to illustrate the obtained results.

In this paper, we establish some best proximity results for Kannan-Chatterjea-Ćirić type contractions in the setting of metric-like spaces. We also provide some concrete examples illustrating the obtained results.