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Zbl 1218.49026
Malinowska, A.B.; Torres, D.F.M.
The Hahn quantum variational calculus. (English)
[J] J. Optim. Theory Appl. 147, No. 3, 419-442 (2010). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.

MSC 2000:: *49K10 Free problems in several independent variables (nec./ suff.)
81Q93

Keywords: Hahn's difference operator; Jackson-Norlünd's integral; quantum calculus; calculus of variations; Leitmann's principle; Ramsey model

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Zentralblatt MATH Berlin [Germany]