In this paper, we introduce the notion of a monotone (\alpha,\beta)-nonexpansive mapping in an ordered Banach space E with the partial order \leq and prove some existence theorems of fixed points of a monotone (\alpha,\beta)-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

    \[\limsup_{n\to\infty}s_n(1-s_n) > 0\quad and \quad \liminf_{n\to\infty}s_n(1-s_n) > 0.\]

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

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Muangchoo-in, Khanitin, Thongtha, Dawud, Cho, Yeol Je, Kumam, Poom