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A Symmetric Nörlund Sum with Application to Inequalities

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Differential and Difference Equations with Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

Abstract

Properties of an α,β-symmetric Nörlund sum are studied. Inspired in the work by Agarwal et al., α,β-symmetric quantum versions of Hölder’s, Cauchy–Schwarz’s and Minkowski’s inequalities are obtained.

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References

  1. Agarwal, R., Bohner, M., Peterson, A.: Inequalities on time scales: a survey. Math. Inequal. Appl. 4(4), 535–557 (2001)

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  2. Aldwoah, K.A.: Generalized time scales and associated difference equations, Ph.D. thesis, Cairo University (2009)

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  3. Brito da Cruz, A.M.C., Martins, N., Torres, D.F.M.: Higher-order Hahn’s quantum variational calculus, Nonlinear Anal. 75(3), 1147–1157 (2012)

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  4. Kac, V., Cheung, P.: Quantum Calculus. Springer, New York (2002)

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  5. Malinowska, A.B., Torres, D.F.M.: The Hahn quantum variational calculus. J. Optim. Theory Appl. 147(3), 419–442 (2010)

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  6. Thomson, B.S.: Symmetric Properties of Real Functions, Dekker, New York (1994)

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Acknowledgements

This work is supported by FEDER and Portuguese funds, COMPETE reference FCOMP-01-0124-FEDER-022690, and CIDMA and FCT, project PEst-C/MAT/UI4106/2011. Brito da Cruz is also supported by FCT through the Ph.D. fellowship SFRH/BD/33634/2009.

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Authors and Affiliations

  1. Escola Superior de Tecnologia de Setúbal, Instituto Politécnico de Setúbal, Estefanilha, 2910-761, Setúbal, Portugal

    Artur M. C. Brito da Cruz

  2. Department of Mathematics, University of Aveiro, Center for Research and Development in Mathematics and Applications, 3810-193, Aveiro, Portugal

    Artur M. C. Brito da Cruz, Natália Martins & Delfim F. M. Torres

Authors
  1. Artur M. C. Brito da Cruz
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  2. Natália Martins
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  3. Delfim F. M. Torres
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Corresponding author

Correspondence to Artur M. C. Brito da Cruz .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Cruz, A.M.C.B.d., Martins, N., Torres, D.F.M. (2013). A Symmetric Nörlund Sum with Application to Inequalities. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_44

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