Abstract We show that the asymptotic regularity and strong convergence of modified Halpern iteration due to T.-H. Kim H.-K. Xu studied further by A. Cuntavenapit B. Panyanak Tikhonov–Mann introduced H. Cheval L. Leuştean as a generalization an Y. Yao et al. has recently been Boţ can be reduced each other in general geodesic settings. This, particular, gives new proof result together with from H...

and Applied Analysis 3 2. Preliminaries Let E be a real Banach space with dual space E∗. When {xn} is a sequence in E, we denote strong convergence of {xn} to x ∈ E by xn → x and weak convergence by xn ⇀ x, respectively. As usual, we denote the duality pairing of E∗ by 〈x, x∗〉, when x∗ ∈ E∗ and x ∈ E, and the closed unit ball by UE, and denote by R and N the set of all real numbers and the set ...

The purpose of this article is to modify normal Mann’s iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.