Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43620171130The second dual of strongly zero-product preserving maps178117901063ENA.R.KhoddamiFaculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran.Journal Article20160228The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are defined. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of a strongly zero-product, strongly Jordan zero-product and strongly Lie zero-product preserving map on a certain class of normed algebras are investigated.http://bims.iranjournals.ir/article_1063_7b8628e66b977698b444316e36a92e54.pdf