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Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

  • Luisa Di Piazza EMAIL logo und Valeria Marraffa
Veröffentlicht/Copyright: 30. November 2017
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 67 Heft 6

Abstract

In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.

MSC 2010: Primary 26E50; Secondary 28E10; 03E72
Keywords: fuzzy Pettis integral; generalized fuzzy number measure; fuzzy weak integrability

The authors were partially supported by the grant of GNAMPA prot. U 2016/000386.

Cordially dedicated to Professor Paolo de Lucia on the occasion of his 80th birthday with esteem and admiration

Communicated by Anatolij Dvurečenskij

Acknowledgement

The authors are grateful to the anonymous reviewers for their valuable remarks.

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Received: 2016-5-16
Accepted: 2016-8-5
Published Online: 2017-11-30
Published in Print: 2017-11-27

© 2017 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
https://doi.org/10.1515/ms-2017-0057
Schlagwörter für diesen Artikel
fuzzy Pettis integral; generalized fuzzy number measure; fuzzy weak integrability

Artikel in diesem Heft

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
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