Copyright © 2011 Hadi Khatibzadeh. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a new discrete version of nonlinear oscillator
with damping dynamical system governed by a general maximal monotone
operator. We show the weak convergence of solutions and their weighted averages
to a zero of a maximal monotone operator . We also prove some strong convergence
theorems with additional assumptions on . This iterative scheme
gives also an extension of the proximal point algorithm for the approximation
of a zero of a maximal monotone operator. These results extend previous
results by Brézis and Lions (1978), Lions (1978) as well as Djafari Rouhani and H. Khatibzadeh (2008).