### The Existence and Approximation Fixed Point Theorems for Monotone Nonspreading Mappings in Ordered Banach Spaces

#### Abstract

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 \(\leq\). 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 \(\sum\limits_{n=1}^\infty\beta_n(1-\beta_n)=\infty\), which contain \(\beta_n=\frac1{n+1}\) as a special case.

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DOI: http://dx.doi.org/10.26713%2Fjims.v11i3-4.419

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