101 citations · 650 across the 25 of their papers we have counts for
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Symmetric Differentiation on Time Scales
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on tim…
Hahn's Symmetric Quantum Variational Calculus
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
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 t…
Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales
Natalia Martins, Delfim F. M. Torres
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions im…
A symmetric Norlund sum with application to inequalities
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
Properties of an -symmetric Norlund sum are studied. Inspired in the work by Agarwal et al., -symmetric quantum versions of Holder, Cauchy-Schwarz and Minkowski inequalit…
Generalized transversality conditions for the Hahn quantum variational calculus
Agnieszka B. Malinowska, Natalia Martins
We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cann…