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On solvability of functional equations and system of functional equations arising in dynamic programming |
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| Authors: | Z Liu S.M Kang |
| Affiliation: | a Department of Mathematics, Liaoning Normal University, PO Box 200, Dalian, Liaoning 116029, PR China b Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6988, USA c Department of Mathematics and RINS, Gyeongsang National University, Chinju 660-701, South Korea |
| Abstract: | The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature. |
| Keywords: | Dynamic programming Functional equation System of functional equations Coincidence solutions Fixed point theorems Iterative approximation Nonexpansive mapping |
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