The purpose of this article is to introduce two iterative algorithms for finding the least norm fixed point of nonexpansive mappings. We provide two algorithms, one implicit and another explicit, from which strong convergence theorems are obtained in Hilbert spaces. Then we apply these algorithms to solve some convex optimization problems. Furthermore, we use them to solve some split feasibility problems. The results of this article extend and improve several results presented in the literature in the recent past. Mathematics Subject Classification (2000): 47H09; 47H10; 90C25.
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