Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 40 No. 1 (2022): Revista Integración, temas de matemáticas
Research and Innovation Articles

Generalized Fractional Ostrowski and Grüss type inequalities involving several Banach algebra valued function

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George A. Anastassiou
University of Memphis
DOI: https://doi.org/10.18273/revint.v40n1-2022007

Published 2022-03-01

Keywords

  • Generalized fractional derivative,
  • generalized fractional inequalities,
  • Ostrowski inequality,
  • Grüss inequality,
  • Banach algebra

How to Cite

Anastassiou, G. A. (2022). Generalized Fractional Ostrowski and Grüss type inequalities involving several Banach algebra valued function. Revista Integración, Temas De matemáticas, 40(1), 119–136. https://doi.org/10.18273/revint.v40n1-2022007

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Creative Commons License

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Abstract

Using generalized Caputo fractional left and right vectorial Taylor formulae, we establish mixed fractional Ostrowski and Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ∥·∥p, 1 ≤p ≤∞.

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References

  1. Aliprantis C. and Border K., Infinite Dimensional Analysis, Springer, 3rd ed., Berlin, 2006. doi: 10.1007/3-540-29587-9
  2. Anastassiou G.A., Fractional Differentiation Inequalities, Springer, 1th ed., New York, 2009. doi: 10.1007/978-0-387-98128-4
  3. Anastassiou G.A., Advances on Fractional Inequalities, Springer, 1th ed., New York, 2011. doi: 10.1007/978-1-4614-0703-4
  4. Anastassiou G.A., Intelligent Comparisons: Analytic Inequalities, Springer, Heidelberg, 1th ed., New York, 2016. doi: 10.1007/978-3-319-21121-3
  5. Anastassiou G.A., Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, 1th ed., New York, 2018. doi: 10.1007/978-3-319-66936-6
  6. Čebyšev P.L., “Sur les expressions approximatives desintégrales définies par les aures prises entre les mêmes limites”, Proc. Math. Soc. Charkov, 2 (1882), 93-98. doi: 10.12691/tjant-2-3-2
  7. Dragomir S.S., “Noncommutative Ostrowski type inequalities for functions in Banach algebras”, in RGMIA Res. Rep. Coll., 24 (2021). https://rgmia.org/papers/v24/v24a10.pdf [cited 5 October, 2021].
  8. Dragomir S.S., “New Noncommutative Grüss type inequalities for functions in Banach algebras”, in RGMIA Res. Rep. Coll., 24 (2021). https://rgmia.org/papers/v24/v24a13.pdf [cited 5 October, 2021].
  9. Mikusinski J., The Bochner integral, Birkhäuser, vol. 55, New York, 1978. doi: 10.1007/978-3-0348-5567-9_3
  10. Ostrowski A., “Über die Absolutabweichung einer differentiabaren Funcktion von ihrem Integralmittelwert”, Comment. Math. Helv., 10 (1938), 226-227.
  11. Rudin W., Functional Analysis, McGraw-Hill, 2nd ed., New York, 1991.