creative_2017_26_2_163_180_001

Fixed point theorems and convergence theorems for monotone ($\alpha,\beta$)-nonexpansive mappings in ordered Banach spaces


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


Abstract

creative_2017_26_2_163_180_abstract

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.

Additional Information

Author(s)

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