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In this paper, we introduce a new iterative midpoint rule for finding a solution of xed point problem for a nonexpansive semigroup in real Hilbert spaces. We establish a strong convergence theorem for the sequences generated by our proposed iterative scheme. Furthermore, we provide application to Fredholm integral equations. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.

A Generalized Nonlinear Iterative Algorithm for the Explicit Midpoint Rule of Nonexpansive Semigroup