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Injective mappings in R-R and lineability



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Jiménez Rodríguez, P. and Maghsoudi, S. and Muñoz-Fernández, Gustavo A. and Seoane-Sepúlveda, Juan B. (2016) Injective mappings in R-R and lineability. Bulletin of the Belgian Mathematical Society - Simon Stevin, 23 (4). pp. 609-623. ISSN 1370-1444

Official URL: https://projecteuclid.org/euclid.bbms/1480993591



It is known that there is not a two dimensional linear space in R-R every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non differentiable functions which gives, as a result, a differentiable function. In this latter case, we are able to show the existence of linear spaces of the largest possible dimension formed by functions enjoying the previous property. By doing this we provide both positive and negative results to the recent field of lineability. Some open questions are also provided.

Item Type:Article
Uncontrolled Keywords:Lineability; Open mapping; Injective function; Special functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:41620
Deposited On:03 Mar 2017 12:49
Last Modified:06 Mar 2017 08:37

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