Abdullah Shoaib

Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space

Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.MSC:46S40, 47H10, 54H25.

Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results.

Common fixed point results for α-ψ-contractions on a metric space endowed with graph

Abdeljawad (Fixed Point Theory Appl., 2013:19) introduced the concept of α-admissible for a pair of mappings. More recently Salimi et al. [Fixed Point Theory Appl., 2013:151] modified the notion of α-ψ-contractive mappings. In this paper we introduce the concept of an α-admissible map with respect to η and modify the α-ψ-contractive condition for a pair of mappings and establish common fixed point results for two, three, and four mappings in a closed ball in complete dislocated metric spaces. As an application, we derive some new common fixed point theorems for ψ-graphic contractions defined on dislocated metric space endowed with a graph as well as preordered dislocated metric space. Some comparative examples are constructed which illustrate the superiority of our results to the existing ones in the literature.MSC: 46S40, 47H10, 54H25.