A unified approach to the asymptotic almost-equivalence of evolution systems without Lipschitz conditions

Abstract We study the asymptotic behavior of almost-orbits of evolution systems in Banach spaces without any continuity assumptions on either the space or the time dependence. We establish, in a unified framework, standard convergence, ergodic convergence and almost-convergence of almost-orbits for both the weak and the strong topologies on the basis of the analogue behavior of orbits.

[1]  I. Miyadera,et al.  On the asymptotic behaviour of almost-orbits of nonlinear contraction semigroups in Banach spaces , 1982 .

[2]  Juan Peypouquet,et al.  Asymptotic equivalence and Kobayashi-type estimates fornonautonomous monotone operators in Banach spaces , 2009 .

[3]  On the asymptotic behavior of a nonlinear contraction semigroup and the resolvent iteration , 1983 .

[4]  Behzad Djafari Rouhani.  Asymptotic behavior of uniformly asymptotically almost nonexpansive curves in a Hilbert space , 2004 .

[5]  W. Kaczor.  Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups , 2002 .

[6]  S. Reich,et al.  Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces , 1979 .

[7]  Juan Peypouquet,et al.  Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces☆ , 2010 .

[8]  Hong-Kun Xu,et al.  Strong asymptotic behavior of almost-orbits of nonlinear semigroups , 2001 .

[9]  W. Takahashi,et al.  Convergence of almost-orbits of nonexpansive semigroups in banach spaces , 2007 .

[10]  Osman Güer.  On the convergence of the proximal point algorithm for convex minimization , 1991 .

[11]  Gang Li,et al.  NONLINEAR ERGODIC THEOREMS FOR ALMOST-ORBITS OF ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES , 2001 .

[12]  Behzad Djafari Rouhani,et al.  Asymptotic behavior for almost-orbits of a reversible semigroup of non-Lipschitzian mappings in a metric space , 2002 .

[13]  Hong-Kun Xu,et al.  Asymptotic behavior of almost-orbits of nonlinear semigroups of non-Lipschitzian mappings in Hilbert spaces , 1993 .

[14]  I. Miyadera.  Nonlinear Ergodic Theorems for Semigroups of Non-Lipschitzian Mappings in Banach Spaces II , 2002 .

[15]  P. Bénilan,et al.  Equations d'évolution dans un espace de Banach quelconque et applications , 1972 .

[16]  Behzad Djafari Rouhani,et al.  Asymptotic behavior for almost-orbits of asymptotically nonexpansive type mappings in a metric space , 2007 .

[17]  M. Crandall.  Nonlinear Evolution Equations. , 1982 .

[18]  George G. Lorentz,et al.  A contribution to the theory of divergent sequences , 1948 .