α⁎-dominated set-valued mappings and some generalised fixed point results

In this paper, we established some fixed point results for a pair of dominated set-valued mappings fulfilling new generalised Ciric type rational contraction on a sequence contained in a closed ball in a complete dislocated b-metric space. As an application, we established the existence of common fixed point of multi α⁎- dominated mappings in ordered complete dislocated b-metric space. Fixed point results with graphic contractions on a closed ball for graph dominated mappings were established. New definition and results for single-valued mappings were also given. Examples were given to demonstrate the variety of obtained results. The obtained results extended and generalised several comparable results in the existing literature.