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Existence Theorems of Solutions for a System of Nonlinear Inclusions with an Application

Abstract

By using the iterative technique and Nadler's theorem, we construct a new iterative algorithm for solving a system of nonlinear inclusions in Banach spaces. We prove some new existence results of solutions for the system of nonlinear inclusions and discuss the convergence of the sequences generated by the algorithm. As an application, we show the existence of solution for a system of functional equations arising in dynamic programming of multistage decision processes.

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Correspondence to Ke-Qing Wu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wu, KQ., Huang, NJ. & Yao, JC. Existence Theorems of Solutions for a System of Nonlinear Inclusions with an Application. J Inequal Appl 2007, 056161 (2007). https://doi.org/10.1155/2007/56161

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Keywords

  • Banach Space
  • Decision Process
  • Functional Equation
  • Dynamic Programming
  • Iterative Algorithm
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