A symmetric Norlund sum with application to inequalities

Abstract

Properties of an $\alpha ,\beta$-symmetric Norlund sum are studied. Inspired in the work by Agarwal et al., $\alpha ,\beta$-symmetric quantum versions of Holder, Cauchy-Schwarz and Minkowski inequalities are obtained.

Submitted 18-Oct-2011; accepted 09-March-2012; to Proceedings of International Conference on Differential & Difference Equations and Applications, in honour of Professor Ravi P. Agarwal, to be published by Springer in the series Proceedings in Mathematics (PROM)

References in corpus (1)

• The Hahn Quantum Variational Calculus

Cited by in corpus (3)

• Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
• Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems
• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus