In this article, some concepts of locally $(\delta ,\phi )$ -dominated mappings, locally $(\delta ,\phi )$ -continuous mappings and $LR-(\delta ,\phi )$ complete dislocated quasi-metric spaces have been introduced. Fixed point results for such mappings under new contractive conditions in these spaces have been established. As an application, fixed point results endowed with order and graph in such spaces have been examined. Furthermore, the results are substantiated with specific examples. Our empirically validated results represent a novel contribution to the existing body of literature.
