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Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space. (English) Zbl 1161.65043

The main purpose of the paper is to study the following iteration scheme:

y n =P(1-β n )x n +β n T 2 (PT 2 ) n-1 x n ,x n+1 =P(1-α n )y n +α n T 1 (PT 1 ) n-1 y n ,

where X is a normed space, C a convex nonempty subset P:XC a nonexpensive retraction of X onto C , T 1 ,T 2 :CX given mappings. The last two theorems yield conditions under which the sequences are weakly respectively strongly convergent.


MSC:
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
46B20Geometry and structure of normed linear spaces