• 1
  • 2
  • 3
  • 4
IPM
30
YEARS OLD

“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 436
School of Mathematics
  Title:   An ergodic theorem for sequences in a Hilbert space
  Author(s):  B. Djafari Rouhani
  Status:   Published
  Journal: Nonlinear Anal. Forum
  Vol.:  4
  Year:  1999
  Pages:   33-48
  Supported by:  IPM
  Abstract:
By suitable modifying our methods in [10], we prove the following nonlinear ergodic theorem, extending H. Brezis and F.E. Browder [4, Theorem 2] and R. Wittmann's mean ergodic theorem [15, Theorem 2.3].
For any sequence (xn)n ≥ 0 in a real Hilbert space H satisfying: (xj|xj+l) ≤ (xk|xk+l)+ϵ(k,l,jk) for all k,l ≥ 0 and jk with ϵ bounded and limk,l,m→∞ϵ(k,l,m)=0, and any strongly regular summation mehtod {an,j}, the sequence yn=∑j=0an,j xj converges strongly to the same limit. Some identifications of the limit are also given.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right