2012/09/07 by Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres · 1 citation
Mathematics · #math.OC #msc:39A13 #msc:49K05
paper · pdf · doi:10.3934/naco.2013.3.77
published as Numer. Algebra Control Optim. 3 (2013), no. 1, 77--94 · This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-2012
arxiv created 2012/09/07 · arxiv updated 2013/01/31
We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.