In this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was constructed based on the kinetics of the amperometric enzyme problem. Finally, the authors show numerical examples to analyze the solution of that problem.
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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