Keywords: Fixed point, left K-sequentially complete dislocated quasi metric space, Closed ball, semi α_{∗}-admissible.

Abstract: The aim of this paper is to introduce semi α_{∗}-admissible proximal multivalued mapping and establish fixed point results satisfying α_{∗}-ψ-contractive conditions in left K-sequentially complete dislocated quasi metric space. We derive some new fixed point theorems under the improve approach of ordered metric space. An example has been constructed to demonstrate the novelty of these results. As an application, we derive some new fixed point theorems for graphic contractions and obtain existence and uniqueness of solutions of integral equations.

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