Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System
نویسندگان
چکیده
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 A. We also prove some strong convergence theorems with additional assumptions on A. 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 .
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