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Convergence of the modified Mann's iterative method for asymptotically κ-strictly pseudocontractive mappings
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 thedoi:10.1186/1687-1812-2011-100 fatcat:5tb6ljonz5d5ho4m6whktdukjy