Fixed point theorems and convergence theorems for monotone (α, β)-nonexpansive mappings in ordered Banach spaces

In this paper, we introduce the notion of a monotone -nonexpansive mapping in an ordered Banach space with the partial order and prove some existence theorems of fixed points of a monotone -nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of Ishikawa type iteration under the control condition

Finally, we give an numerical example to illustrate the main result in this paper.