In this paper, we introduce
the concept of monotone
α-nonexpansive mappings in an ordered Banach space
E with
the partial order ≤, which contains monotone nonexpansive mappings as special case. With
the help of
the Mann iteration, we show some existence
theorems of fixed points of monotone
α-nonexpansive mappings in uniformly convex ordered Banach space. Also, we prove some weak and strong convergence
theorems of
the Mann iteration for finding an order fixed point of monotone
α-nonexpansive mappings under
the condition
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