In This Article, We Manage Iterative Methods For Approximation of Fixed Points and Their Applications. We Initially Talk About Fixed Point Theorems For a Non-Expansive Mapping or a Group of Non-Expansive Mappings. Specifically, We Express a Fixed Point Hypothesis Which Addressed Certifiably a Problem Posed During the Conference on Fixed Point Theory. We Manage Weak and Strong Union Theorems of Mann's Compose and Halpern's Write In a Banach Space. at Last, Utilizing These Results, We Consider the Plausibility Problem By Raised Blends of Non-Expansive Withdrawals and the Curved Minimization Problem of Finding a Minimizer of an Arched Function.