Strong convergence of halpern's type iteration for -nonexpansive semigroup in banach spaces and cat(0) spaces

In this paper, we establish strong convergence of the Halpern's type iteration for a semigroup of alpha-nonexpansive mappings in Banach spaces. Using the concept of quasilinearization, we extend this result to CAT (0) spaces, an important subclass of metric spaces. Our work generalizes and complements several comparable results existing in the literature.