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Mediterranean Journal of Mathematics

, Volume 10, Issue 2, pp 823–842 | Cite as

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

  • Antonio BoccutoEmail author
  • Xenofon Dimitriou
Article

Abstract

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.

Mathematics Subject Classification (2010)

Primary 41A35 Secondary 46E30 47G10 

Keywords

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

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaPerugiaItaly
  2. 2.Department of MathematicsUniversity of AthensAthensGreece

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