## Topological Methods in Nonlinear Analysis

### On properties of solutions for a functional equation

#### Abstract

This paper studies properties of solutions for a functional equation arising in dynamic programming of multistage decision processes. Using the Banach fixed point theorem and the Mann iterative methods, we prove the existence and uniqueness of solutions and convergence of sequences generated by the Mann iterative methods for the functional equation in the Banach spaces $BC(S)$ and $B(S)$ and the complete metric space $BB(S)$, and discuss behaviors of solutions for the functional equation in the complete metric space $BB(S)$. Four examples illustrating the results presented in this paper are also provided.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 113-133.

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343888

Digital Object Identifier
doi:10.12775/TMNA.2015.040

Mathematical Reviews number (MathSciNet)
MR3443681

Zentralblatt MATH identifier
1366.49030

#### Citation

Liu, Zeqing; Kang, Shin Min. On properties of solutions for a functional equation. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 113--133. doi:10.12775/TMNA.2015.040. https://projecteuclid.org/euclid.tmna/1459343888

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