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Abstract
In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.
MSC (2010) Classification::
Acknowledgements
The authors would like to express their gratitude to the referees and the editors for their helpful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. Email: [email protected]
2. Email: [email protected]
Additional information
Funding
The first author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology [grant number NRF-2010-0013784]. The second and third authors were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [grant number NRF-2012R1A1A2009512].