Uniform modular integrability and convergence properties for a class of Urysohn integral operators in function spaces

Carlo Bardaro; Ilaria Mantellini

Mathematica Slovaca (2006)

  • Volume: 56, Issue: 4, page 465-482
  • ISSN: 0232-0525

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Bardaro, Carlo, and Mantellini, Ilaria. "Uniform modular integrability and convergence properties for a class of Urysohn integral operators in function spaces." Mathematica Slovaca 56.4 (2006): 465-482. <http://eudml.org/doc/31825>.

@article{Bardaro2006,
author = {Bardaro, Carlo, Mantellini, Ilaria},
journal = {Mathematica Slovaca},
keywords = {uniform modular integrability; modular space; nonlinear operator; singularity},
language = {eng},
number = {4},
pages = {465-482},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Uniform modular integrability and convergence properties for a class of Urysohn integral operators in function spaces},
url = {http://eudml.org/doc/31825},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Bardaro, Carlo
AU - Mantellini, Ilaria
TI - Uniform modular integrability and convergence properties for a class of Urysohn integral operators in function spaces
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 4
SP - 465
EP - 482
LA - eng
KW - uniform modular integrability; modular space; nonlinear operator; singularity
UR - http://eudml.org/doc/31825
ER -

References

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  1. BARDARO C.-MANTELLINI I., A modular convergence theorem for nonlinear integral operators, Comment. Math. Prace Mat. 36 (1996), 27-37. (1996) MR1427818
  2. BARDARO C.-MANTELLINI I., On a singularity concept for kernels of nonlinear integral operators, Int. Math. J. 1 (2002), 239-254. Zbl0982.47033MR1840601
  3. BARDARO C.-MANTELLINI I., On approximation properties of Urysohn integral operators, Int. J. Pure Appl. Math. 3 (2002), 129-148. Zbl1012.41017MR1937645
  4. BARDARO C.-MANTELLINI I., Approximation properties in abstract modular spaces for a class of general sampling type operators, Appl. Anal. 85 (2006), 383-413. Zbl1089.41012MR2196677
  5. BARDARO C.-MUSIELAK J.-VINTI G., On absolute continuity of a modular connected with strong summability, Comment. Math. Prace Mat. 34 (1994), 21-33. (1994) Zbl0832.46020MR1325071
  6. BARDARO C.-MUSIELAK J.-VINTI G., Nonlinear Integral Operators and Applications, de Gruyter Ser. Nonlinear Anal. Appl. 9, de Gruyter, Berlin, 2003. Zbl1030.47003MR1994699
  7. BUTZER P. L.-NESSEL R. J., Fourier Analysis and Approximation I, Academic Press, New York-London, 1971. (1971) MR0510857
  8. KOZLOWSKI W. M., Modular Function Spaces, Pure and Applied Math. 122, Marcel Dekker, New York-Basel, 1988. (1988) Zbl0747.46022MR1474499
  9. MANTELLINI I., Generalized sampling operators in modular spaces, Comment. Math. Prace Mat. 38 (1998), 77-92. (1998) Zbl0984.47025MR1672252
  10. MANTELLINI I.-VINTI G., Approximation results for nonlinear integral operators in modular spaces and applications, Ann. Polon. Math. 46 (2003), 55-71. Zbl1019.41013MR1977761
  11. MUSIELAK J., Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034. Springer-Verlag, New York, 1983. (1983) Zbl0557.46020MR0724434
  12. MUSIELAK J., Nonlinear approximation in some modular function spaces I, Math. Japon. 38 (1993), 83-90. (1993) Zbl0779.46017MR1204187
  13. WILLARD S., General Topology Addison-Wesley Series in Math., Addison Wesley Publ. Comp., Reading, MA, 1970. (1970) MR0264581

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