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Let K be a nonempty closed convex subset of a uniformly convex Banach space E with a uniformly Gâteaux differentiable norm. Suppose that T:K→K is an asymptotically non-expansive mapping and for arbitrary initial value x0∈K, we will introduce the Mann iteration of its Cesàro means: xn+1=αnxn+(1−αn)1n+1∑j=0nTjxn,n≥0, and prove its strong and weak convergence whenever ∑n=0∞bn<+∞ and {αn} is a real...
We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings T in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path zt∈tu+(1−t)Tzt.
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