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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 706585, 9 pages
http://dx.doi.org/10.1155/2014/706585
Research Article

Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming

School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India

Received 4 January 2014; Revised 5 March 2014; Accepted 5 March 2014; Published 8 April 2014

Academic Editor: Nawab Hussain

Copyright © 2014 Deepmala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces BC(S) and B(S) and complete metric space BB(S), respectively. Our main results extend, improve, and generalize the results due to several authors. Some examples are also given to demonstrate the advantage of our results over existing one in the literature.