Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

1997 ◽  
Vol 42 (1) ◽  
pp. 8-11 ◽  
Author(s):  
Gang Li ◽  
Jipu Ma
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Lipschitzian Mappings ◽  
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.

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