Some functional equations in the theory of dynamic programming. I. Functions of points and point transformations

Author:
R. Bellman

Journal:
Trans. Amer. Math. Soc. **80** (1955), 51-71

MSC:
Primary 39.0X

DOI:
https://doi.org/10.1090/S0002-9947-1955-0074692-0

MathSciNet review:
0074692

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References | Similar Articles | Additional Information

**[1]**K. J. Arrow, T. E Harris, and J. Marschak,*Optimal inventory policy*, Cowles Commission Paper No. 44, 1951.**[2]**Richard Bellman,*Bottleneck problems, functional equations, and dynamic programming*, Econometrica**23**(1955), 73–87. MR**0070935**, https://doi.org/10.2307/1905582**[3]**Richard Bellman,*Dynamic programming and a new formalism in the theory of integral equations*, Proc. Nat. Acad. Sci. U.S.A.**41**(1955), 31–34. MR**0072365****[4]**Richard Bellman,*Stability theory of differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. MR**0061235****[5]**-,*A survey of the theory of boundedness, stability and asymptotic behavior of linear and nonlinear differential and difference equations*, Office of Naval Research, 1949.**[6]**-,*Dynamic programming, mathematics for modern engineers*, ed. by E. F. Beckenbach, McGraw-Hill, Chapter 12, to appear.**[7]**-,*Dynamic programming. A survey*, Operations Research Quarterly vol. 2 (1954) pp. 275-284.**[8]**Richard Bellman,*On the theory of dynamic programming*, Proc. Nat. Acad. Sci. U. S. A.**38**(1952), 716–719. MR**0050856****[9]**Richard Bellman,*Some problems in the theory of dynamic programming*, Econometrica**22**(1954), 37–48. MR**0060709**, https://doi.org/10.2307/1909830**[10]**Richard Bellman,*Some functional equations in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U. S. A.**39**(1953), 1077–1082. MR**0061806****[11]**Richard Bellman,*The theory of dynamic programming*, Bull. Amer. Math. Soc.**60**(1954), 503–515. MR**0067459**, https://doi.org/10.1090/S0002-9904-1954-09848-8**[12]**-,*On the optimal inventory equation*, Management Science (to appear).**[13]**Richard Bellman,*Dynamic programming and a new formalism in the calculus of variations*, Proc. Nat. Acad. Sci. U. S. A.**40**(1954), 231–235. MR**0061289****[14]**-,*On computational problems in the theory of dynamic programming*, Proc. Symposium on Numerical Methods, Santa Monica, 1953, New York, McGraw-Hill, 1955.**[15]**Richard Bellman,*Monotone approximation in dynamic programming and the calculus of variations*, Proc. Nat. Acad. Sci. U. S. A.**40**(1954), 1073–1075. MR**0067344****[16]**R. Bellman and D. Blackwell,*On a particular non-zero-sum game*, September, 1949 (unpublished).**[17]**R. Bellman and J. P. LaSalle,*On non-zero-sum games and stochastic processes*, August, 1949 (unpublished).**[18]**Richard Bellman and Shermann Lehman,*On the continuous gold-mining equation*, Proc. Nat. Acad. Sci. U. S. A.**40**(1954), 115–119. MR**0060681****[19]**-,*A functional equation in the theory of dynamic programming and its generalizations*(submitted to Memoirs of the American Mathematical Society).**[20]**A. Dvoretzky, J. Kiefer, and J. Wolfowitz,*The inventory problem. I. Case of known distributions of demand*, Econometrica**20**(1952), 187–222. MR**0047304**, https://doi.org/10.2307/1907847

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DOI:
https://doi.org/10.1090/S0002-9947-1955-0074692-0

Article copyright:
© Copyright 1955
American Mathematical Society