Functional equations in the theory of dynamic programming—XII: Complex operators and min-max variation

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Functional equations in the theory of dynamic programming—XII: Complex operators and min-max variation

Richard Bellman and R. Sherman Lehman

Source: Duke Math. J. Volume 28, Number 3 (1961), 335-343.

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See also: Richard Bellman, Sherman Lehman. Functional equations in the theory of dynamic programming— X : Resolvents, characteristic functions and values. Duke Math. J. Vol. 27, No. 1 (1960), pp. 55–69.

Project Euclid: euclid.dmj/1077468916

See also: Richard Bellman. Some functional equations in the theory of dynamic programming. I. Functions of points and point transformations. Trans. Amer. Math. Soc. Vol. 80 (1955), pp. 51–71.

Mathematical Reviews (MathSciNet): MR0074692

See also: Richard Bellman. Functional equations in the theory of dynamic programming. II. Nonlinear differential equations. Proc. Nat. Acad. Sci. USA Vol. 41 (1955), pp. 482–485.

Mathematical Reviews (MathSciNet): MR0072314

See also: Richard Bellman. Functional equations in the theory of dynamic programming. III. Rend. Circ. Mat. Palermo Vol. 5 (1956), pp. 297–319 (1957).

Mathematical Reviews (MathSciNet): MR0087876

See also: Richard Bellman. Functional equations in the theory of dynamic programming. V. Positivity and quasi-linearity. Proc. Nat. Acad. Sci. USA Vol. 41 (1955), pp. 743–746.

Mathematical Reviews (MathSciNet): MR0074693

See also: Richard Bellman. Functional equations in the theory of dynamic programming. VI. A direct convergence proof. Ann. of Math. Vol. 65 (1957), pp. 215-223.

Mathematical Reviews (MathSciNet): MR0083675

See also: Richard Bellman. Functional equations in the theory of dynamic programming. VII. A partial differential equation for the Fredholm resolvent. Proc. Amer. Math. Soc. Vol. 8 (1957), pp. 435–440.

Mathematical Reviews (MathSciNet): MR0088666

See also: Richard Bellman. Functional equations in the theory of dynamic programming. VIII. The variation of Green’s functions for the one-dimensional case. Proc. Nat. Acad. Sci. USA Vol. 43 (1957) pp. 839–841.

Mathematical Reviews (MathSciNet): MR0093619

See also: Richard Bellman, Sherman Lehman. Functional equations in the theory of dynamic programming—IX: Variational analysis, analytic continuation, and imbedding of operators. Proc. Nat. Acad. Sci. USA Vol. 44 (1958), pp. 905–907.

Mathematical Reviews (MathSciNet): MR0097639

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XI. Limit theorems. Rend. Circ. Mat. Palermo Vol. 8 (1959), pp. 343–345.

Mathematical Reviews (MathSciNet): MR0114069

See also: Richard Bellman, William Karush. Functional equations in the theory of dynamic programming. XII. An application of the maximum transform. J. Math. Anal. Appl. Vol. 6 (1963), pp. 155–157.

Mathematical Reviews (MathSciNet): MR0146001

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XIII. Stability considerations. J. Math. Anal. Appl. Vol. 12 (1965), pp. 537–540.

Mathematical Reviews (MathSciNet): MR0191703

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XIV. Upper and lower bounds for solutions of nonlinear partial differential equations. J. Math. Anal. Appl. Vol. 27 (1969), pp. 461–468.

Mathematical Reviews (MathSciNet): MR0244819

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XV. Layered functionals and partial differential equations. J. Math. Anal. Appl. Vol. 28 (1969), pp. 1–3.

Mathematical Reviews (MathSciNet): MR0250155

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XVI. An equation involving iterates. J. Math. Anal. Appl. Vol. 30 (1970), pp. 592–595.

Mathematical Reviews (MathSciNet): MR0260416

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XVII. Policies dependent on critical state variables. J. Math. Anal. Appl. Vol. 33 (1971), pp. 231–233.

Mathematical Reviews (MathSciNet): MR0270733

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XVIII. Minimum convolutions and Green’s functions. J. Math. Anal. Appl. Vol. 33 (1971), pp. 497–499.

Mathematical Reviews (MathSciNet): MR0275861

See also: Richard Bellman. Functional equations in the theory of dynamic programming. XIX [printed as XVIII]. A problem connected with the value of information. Math. Biosci. Vol. 11 (1971), pp. 1–3.

Mathematical Reviews (MathSciNet): MR0285263

Primary Subjects: 90.58

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077469692
Mathematical Reviews number (MathSciNet): MR0134352
Zentralblatt MATH identifier: 0102.15602
Digital Object Identifier: doi:10.1215/S0012-7094-61-02830-7

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