Ishikawa Iteration Process for Approximating Fixed Points of Nonexpansive Mappings

Abstract:

      Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.If T:C→C is a nonexpansive mapping.then for any initial data x₀∈C,the Ishikawaiteration process {x_n},defined by x_n=t_nT(s_nTx_n+(1-s_n)x_n)+(1-t_n)x_n,n≥0,converges weakly to a fixed point of T,where{t_n}and{s_n}are sequences in[0,1]withsome restrictions.