Fixed point results for (alpha )-(psi )-locally graphic contraction in dislocated qusai metric spaces

In this paper, we have obtained fixed point results for (alpha -psi ) -locally contractive type mappings in a closed ball in left (K)-sequentially complete and in right (K)-sequentially complete dislocated quasi metric spaces. Moreover the mappings under consideration are (alpha )-admissible with respect to (eta ). We have used conditions weaker than those of Samet et al. [Nonlinear Anal. 75:2154–2165, (2012)]. As an application, we have derived some new fixed point theorems for (psi ) -graphic contractions defined on dislocated quasi metric space endowed with a graph as well as ordered dislocated metric space. Some comparative examples are constructed which illustrate the superiority of our results. In the process we have generalized several well known, recent and classical results from the literature.