Strong and weak convergences in 2-probabilistic normed spaces

Abstract

In this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed spaces (2-PN spaces) and established some of its properties. Later, we have defined the strong and weak boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient condition for the linear map between two 2-PN spaces to be strongly and weakly bounded.

Keywords

• Menger
• linear 2-normed spaces
• triangle functions
• t-norms

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