Modular filter convergence theorems for Urysohn integral operators and applications

作者：Boccuto Antonio^*; Dimitriou Xenofon

来源：Acta Mathematica Sinica-English Series, 2013, 29(6): 1055-1066.

DOI：10.1007/s10114-013-1443-6

• Egorov filter
• Lebesgue filter
• filter convergence
• filter exhaustiveness
• filter singularity
• integral operator
• Mellin operator
• modular convergence
• modular space

We prove some versions of modular convergence theorems for nonlinear Urysohn-type integral operators with respect to filter convergence. We consider pointwise filter convergence of functions giving also some applications to linear and nonlinear Mellin operators. We show that our results are strict extensions of the classical ones.

• 出版日期2013-6