Convergence of the modified Mann's iterative method for asymptotically κ-strictly pseudocontractive mappings

Ying Zhang, Zhiwei Xie
2011 Fixed Point Theory and Applications  
Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I -T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann's algorithm for T under suitable control conditions. Moreover, we also elicit a necessary and sufficient condition that guarantees strong convergence of the
more » ... ified Mann's iterative sequence to a fixed point of T in a real Banach spaces with the Fréchet differentiable norm. 2000 AMS Subject Classification: 47H09; 47H10.
doi:10.1186/1687-1812-2011-100 fatcat:5tb6ljonz5d5ho4m6whktdukjy