The Existence and Approximation Fixed Point Theorems for Monotone Nonspreading Mappings in Ordered Banach Spaces (Journal of Informatics and Mathematical Sciences, 2019)
In this paper, we proved some existence theorems of fixed points for monotone nonspreading mappings \(T\) in a Banach space \(E\) with the partial order \(≤\). In order to finding a fixed point of such a mapping \(T\), moreover we proved the convergence theorem of Mann iterative schemes under the condition \(\sum\limits_{n=1}^∞β_n(1-β_n)=∞\), which contain \(β_n=\frac1{n+1}\) as a special case.
Keywords: Ordered Banach space; Fixed point; Monotone nonspreading mapping; Mann iterative scheme