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The aim of this paper is to investigate bounded linear functionals on an n-normed space with respect to norms of its quotient spaces. These norms will be our main tools as well as a new viewpoint. We will give several types of boundedness of bounded linear functionals on an n-normed space and investigate the dual spaces that corresponds to each type of boundedness. We obtain the relations between all types of boundedness, which correspond to the inclusion relations between the dual spaces.

Bounded Linear Functional on n-Normed Spaces through Its Quotient Spaces