A generalized nonlinear iterative algorithm for the explicit midpoint rule of nonexpansive semigroup

Abstract

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. Anumerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.