In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results.

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<abstract><p>In 2017, the concepts of orthogonal set and orthogonal metric spaces are presented. And an extension of Banach fixed point theorem is proved in this type metric spaces. Further in 2019, on orthogonal metric spaces, some fixed point theorems via altering distance functions are investigated. In this paper, presence and uniqueness of fixed points of the generalizations of contraction principle via auxiliary functions are investigated. And some consequences and an illustrative example are presented. On the other hand, homotopy theory constitute an important area of algebraic topology, but the application of fixed point results in orthogonal metric spaces to homotopy has not been done until now. As a different application in this field, the homotopy application of the one of the corollaries is given at the end of this paper.</p></abstract>

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