scholarly journals A nonlinear ergodic theorem for discrete systems

1994 ◽  
Vol 32 (3) ◽  
pp. 179-191 ◽  
Author(s):  
Kathleen M. Crowe
Keyword(s):  
Ergodic Theorem ◽  
Discrete Systems ◽  
Nonlinear Ergodic Theorem

Fixed Point Theorem and Nonlinear Ergodic Theorem for Nonexpansive Semigroups Without Convexity

1992 ◽  
Vol 44 (4) ◽  
pp. 880-887 ◽  
Author(s):  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Ergodic Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Nonexpansive Semigroups ◽  
Amenable Semigroups ◽  
Nonlinear Ergodic Theorem

AbstractWe first prove a nonlinear ergodic theorem for nonexpansive semigroups without convexity in a Hilbert space. Further we prove a fixed point theorem for non-expansive semigroups without convexity which generalizes simultaneously fixed point theorems for left amenable semigroups and left reversible semigroups.

Weak and strong convergence theorems and a nonlinear ergodic theorem for N-generalized hybrid mappings

2017 ◽  
Vol 10 (01) ◽  
pp. 1750001
Author(s):  
Sattar Alizadeh ◽  
Fridoun Moradlou
Keyword(s):  
Weak Convergence ◽  
Strong Convergence ◽  
Ergodic Theorem ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Strong Convergence Theorem ◽  
Weak And Strong Convergence ◽  
Weak Convergence Theorem ◽  
Nonlinear Ergodic Theorem ◽  
Nonlinear Mappings

In this paper, assuming an appropriate condition, we prove that [Formula: see text]-generalized hybrid mappings are demiclosed in Hilbert spaces. Using this fact, we prove a weak convergence theorem of Ishikawa type for these nonlinear mappings. Also, a strong convergence theorem of Halpern–Ishikawa type and a nonlinear ergodic theorem for [Formula: see text]-generalized hybrid mappings have been proven in Hilbert spaces.

A UNIFORM QUANTITATIVE FORM OF SEQUENTIAL WEAK COMPACTNESS AND BAILLON'S NONLINEAR ERGODIC THEOREM

2012 ◽  
Vol 14 (01) ◽  
pp. 1250006 ◽  
Author(s):  
ULRICH KOHLENBACH
Keyword(s):  
Ergodic Theorem ◽  
Weak Compactness ◽  
Subsequent Paper ◽  
Extended Sense ◽  
Quantitative Form ◽  
Complexity Estimate ◽  
Sequential Compactness ◽  
Nonlinear Ergodic Theorem ◽  
Primitive Recursive ◽  
Gödel’S T

We apply proof-theoretic techniques of "proof mining" to obtain an effective uniform rate of metastability in the sense of Tao for Baillon's famous nonlinear ergodic theorem in Hilbert space. In fact, we analyze a proof due to Brézis and Browder of Baillon's theorem relative to the use of weak sequential compactness. Using previous results due to the author we show the existence of a bar recursive functional Ω* (using only lowest type bar recursion B0, 1) providing a uniform quantitative version of weak compactness. Primitive recursively in this functional (and hence in T0 + B0, 1) we then construct an explicit bound φ on for the metastable version of Baillon's theorem. From the type level of φ and another result of the author it follows that φ is primitive recursive in the extended sense of Gödel's T. In a subsequent paper also Ω* will be explicitly constructed leading to the refined complexity estimate φ ∈ T4.

Sign in / Sign up

Export Citation Format

Share Document