A nonstandard proof of a generalized demiclosedness principle Dedicated to

LetX be a uniformly convex Banach space, C a nonempty, closed and convex subset of X and let T : C → X be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we present a nonstandard proof of a demiclosedness principle for such T .

[1]  Sims GARCIA-FALSET,et al.  THE DEMICLOSEDNESS PRINCIPLE FOR MAPPINGS OF ASYMPTOTICALY NONEXPANSIVE TYPE , 2007 .

[2]  C. E. Chidume,et al.  THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS CONVERGENCE THEOREMS FOR MAPPINGS WHICH ARE ASYMPTOTICALLY NONEXPANSIVE IN THE INTERMEDIATE SENSE , 2003 .

[3]  S. Reich,et al.  A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense , 2001 .

[4]  W. A. Kirk,et al.  An Introduction to Metric Spaces and Fixed Point Theory , 2001 .

[5]  B. Sims,et al.  Ultra-Methods in Metric Fixed Point Theory , 2001 .

[6]  H. Oka.  An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense , 1997 .

[7]  Simeon Reich,et al.  Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property , 1993 .

[8]  Hong-Kun Xu,et al.  Existence and convergence for fixed points of mappings of asymptotically nonexpansive type , 1991 .

[9]  Brailey Sims,et al.  Ultra-techniques in Banach space theory , 1982 .

[10]  William A. Kirk,et al.  Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type , 1974 .

[11]  William A. Kirk,et al.  A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 1972 .

[12]  Felix E. Browder,et al.  Semicontractive and semiaccretive nonlinear mappings in Banach spaces , 1968 .

[13]  R. Demarr,et al.  Common fixed points for commuting contraction mappings , 1963 .

[14]  J. A. Clarkson.  Uniformly convex spaces , 1936 .