Inspired by the notion of the parallel sum for operators and given two mappings P and Q, we propose a modified definition of their parallel sum and proceed to establish some properties of this new mapping. Some connections are then made with the resolvent of monotone operators and other nonlinear applied analysis concepts. Algorithmic approaches are suggested and some remarks and questions are also stated.
Moudafi, A., Ramazannejad, M., A new approach of the parallel sum: Properties and algorithmic aspects, <<COMMUNICATIONS ON APPLIED NONLINEAR ANALYSIS>>, 2015; 22 (2): 46-57 [https://hdl.handle.net/10807/325318]
A new approach of the parallel sum: Properties and algorithmic aspects
Ramazannejad, Maede
2015
Abstract
Inspired by the notion of the parallel sum for operators and given two mappings P and Q, we propose a modified definition of their parallel sum and proceed to establish some properties of this new mapping. Some connections are then made with the resolvent of monotone operators and other nonlinear applied analysis concepts. Algorithmic approaches are suggested and some remarks and questions are also stated.
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