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In this article, we have designed two existence of fixed point theorems which are regarding to set-valued SU-type  θ η -contraction and  Γ α -contraction via gauge function in the setting of metric spaces. An extensive set of nontrivial example will be given to justify our claim. At the end, we will give an application to prove the existence behavior for the system of functional equation in dynamical system and integral inclusion.

Set-Valued SU-Type Fixed Point Theorems via Gauge Function with Applications