Existence and Iterative Approximations of Solutions for Certain Functional Equation and Inequality

Existence and Iterative Approximations of Solutions for Certain Functional Equation and Inequality

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Article ID: iaor20132842
Volume: 157
Issue: 3
Start Page Number: 716
End Page Number: 736
Publication Date: Jun 2013
Journal: Journal of Optimization Theory and Applications
Authors: , , ,
Keywords: programming: dynamic
Abstract:

This paper deals with a functional equation and inequality arising in dynamic programming of multistage decision processes. Using several fixed‐point theorems due to Krasnoselskii, Boyd–Wong and Liu, we prove the existence and/or uniqueness and iterative approximations of solutions, bounded solutions and bounded continuous solutions for the functional equation in two Banach spaces and a complete metric space, respectively. Utilizing the monotone iterative method, we establish the existence and iterative approximations of solutions and nonpositive solutions for the functional inequality in a complete metric space. Six examples which dwell upon the importance of our results are also included.

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