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Muayad G. Mohsin, Z. D. Al-Nafie,
Differentiability of Mappings of Locally Convex Algebras.
Int. J. Math. Comput. Sci., 20, no. 1, (2025), 17-22


Keywords and phrases:

Linear mapping, Topological algebra, Topological Vector Space, Differentiablity, Convex Space, Jointly Continuous.


In this work, we introduce the notion of sigma-differentiability and (A_{1},sigma)-differentiability of mappings in locally convex algebras. Moreover, we establish sigma-continuous and (A_{1},\sigma)-continuous mappings in these algebras associated with a system of bounded subsets in a convex algebra. In particular, we extend the method of Averbuch and Smolyanov to introduce a new approach of differentiability in topological algebras that is carried by a locally convex topology.