On Reverses of Some Inequalities in n-Inner Product Spaces

In 1964, Gähler 1 introduced the concept of 2-norm and 2-inner product spaces as generalization of norm and inner product spaces. A systematic presentation of the results related to the theory of 2-inner product spaces can be found in the book in 2, 3 and in list of references in it. Generalization of 2-inner product space for n ≥ 2 was developed by Misiak 4 in 1989. Gunawan and Mashadi 5 in 2001 introduced the concept of n-normed linear spaces. Gunawan 6 obtained Cauchy-Bunyakovsky inequality in these spaces. Cho et al. 7 extended parallelogram law and proved Hlwaka’s type inequality in n-inner product spaces. In this paper by, using same ideas of 8–13 we establish some results regarding new reverses of Cauchy-Bunyakovsky-Schwarz inequality, and Triangle and Boas-Bellman Type inequalities in n-inner product spaces and we also provide some applications for determinantal integral inequalities.