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]**R. Bellman,*Bottleneck problems, functional equations and dynamic programming*, Econometrica vol. 23 (1955) pp. 73-87. MR**0070935 (17:58e)****[3]**-,*Dynamic programming and a new formalism in the theory of integral equations*, Proc. Nat. Acad. Sci. U.S.A. vol. 41 (1955) pp. 31-34. MR**0072365 (17:272d)****[4]**-,*Stability theory of differential equations*, McGraw-Hill, 1953. MR**0061235 (15:794b)****[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]**-,*The theory of dynamic programming*, Nat. Proc. Acad. Sci. U.S.A. vol. 38 (1952) pp. 716-719. MR**0050856 (14:392b)****[9]**-,*Some problems in the theory of dynamic programming*, Econometrica vol. 22 (1954) pp. 37-48. MR**0060709 (15:713c)****[10]**-,*Some functional equations in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 1077-1082. MR**0061806 (15:887f)****[11]**-,*The theory of dynamic programming*, Bull. Amer. Math. Soc. vol. 60 (1954) pp. 503-515. MR**0067459 (16:732c)****[12]**-,*On the optimal inventory equation*, Management Science (to appear).**[13]**-,*Dynamic programming and a new formalism in the calculus of variations*, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 231-235. MR**0061289 (15:804f)****[14]**-,*On computational problems in the theory of dynamic programming*, Proc. Symposium on Numerical Methods, Santa Monica, 1953, New York, McGraw-Hill, 1955.**[15]**-,*Monotone convergence in dynamic programming and the calculus of variations*, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 1073-1075. MR**0067344 (16:714e)****[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]**R. Bellman and S. Lehmann,*On the continuous gold-mining equation*, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 115-119. MR**0060681 (15:708c)****[19]**-,*A functional equation in the theory of dynamic programming and its generalizations*(submitted to Memoirs of the American Mathematical Society).**[20]**A. J. Dvoretzky, J. Kiefer, and J. Wolfowitz,*The inventory problem*--I:*Case of known distributions of demand and The inventory problem*--II:*Case of unknown distributions of Demand*, Econometrica vol. 20 (1952) pp. 187-222. MR**0047304 (13:856a)**

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

Article copyright:
© Copyright 1955
American Mathematical Society