In this article, we establish fixed point results for a pair of multivalued mappings satisfying generalized contraction on a sequence in dislocated -quasi metric spaces and * Khan type contraction on a sequence in -quasi metric spaces. An example and an application have been discussed. Our results modify and generalize many existing results in literature.

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The aim of this work is to introduce double controlled dislocated quasi-metric type spaces and to obtain fixed point results for a pair of multivalued mappings satisfying Kannan-type double controlled contraction in such spaces. An example has been built and a remark has been given which shows that how our result can be used when a corresponding new result in dislocated quasi b-metric type spaces cannot be used. Our results generalize and extend many existing results in the literature.

Abdeljawad et al. (2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended b-metric spaces. In this paper, we extend their concept and introduce the concept of double controlled quasi-metric type spaces with two incomparable functions and prove some unique fixed point results involving new types of contraction conditions. Also, we introduce the concept of α−μ−k double controlled contraction and prove some related fixed point results. We give several examples to show that our results are the proper generalization of the existing works.

<abstract><p>The main purpose of this research is to establish a new generalized $ \xi^{\ast } $-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $ K $-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.</p></abstract>