The purpose of this paper is to find out fixed point results for a pair of semi ${\alpha }_{*}$ -dominated multivalued mappings fulfilling a generalized locally F-dominated multivalued contractive condition on a closed ball in complete dislocated b-metric space. Some new fixed point results with graphic contractions on closed ball for a pair of multi graph dominated mappings on dislocated b-metric space have been established. An application to the existence of unique common solution of a system of integral equations is presented. 2010 Mathematics Subject Classification: 46Txx, 47H04, 47H10; 54H25.

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

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.

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.

The purpose of this paper is to find out fixed point results for semi-α⁎-dominated multivalued mappings fulfilling a new generalized locallyF-dominated multivalued contractive condition on a closed ball in complete dislocated metric space. Example and application both are given to show the novelty of our results. Our results merge, extend, and infer many results.