The implicit midpoint rule for nonexpansive mappings
Maryam A Alghamdi, Mohammad Ali Alghamdi, Naseer Shahzad, Hong‐Kun Xu · Fixed Point Theory and Applications · 2014
Abstract The implicit midpoint rule (IMR) for nonexpansive mappings is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications to the periodic solution of a nonlinear time-dependent evolution equation and to a Fredholm integral equation are included. MSC:47J25, 47N20, 34G20, 65J15.