In this paper, we introduce the concept of -dominated multivalued mappings and establish the existence of common fixed
points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These
results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not
only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive
conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application,
we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued
mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions
on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation.