Modular Convergence Theorems for Integral Operators in the Context of Filter Exhaustiveness and Applications

作者：Boccuto Antonio^*; Dimitriou Xenofon

来源：Mediterranean Journal of Mathematics, 2013, 10(2): 823-842.

DOI：10.1007/s00009-012-0199-z

• filter convergence
• filter exhaustiveness
• integral operator
• moment operator
• Mellin operator
• Mellin-Gauss-Weierstrass operator
• Mellin-Poisson-Cauchy operator
• modular
• modular convergence
• filter singularity

We prove some modular convergence theorems for nonlinear Urysohn-type integral operators, applying filter convergence of sequences of functions. We give some applications to Mellin operators, including moment, Mellin-Poisson-Cauchy and Mellin-Gauss-Weierstrass operators. We show that our results are proper extensions of the classical ones, and we pose an open problem.

• 出版日期2013-5