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Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. (English) Zbl 1137.47053

The paper gives significant generalizations of results concerning a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings. The authors establish a necessary and sufficient condition for the convergence of the iteration scheme to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings in a Banach space. They also prove weak and strong convergence results for the iteration scheme to a common fixed point of a finite family of \(\left(L-\gamma\right)\) uniform Lipschitz and asymptotically quasi-nonexpansive mappings in uniformly convex Banach spaces.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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