The Quotient Inequalities

Benedict Barnes, C. Sebil, I. K. Dontwi

Abstract

This paper contributes to the inequalities, specifically, the relationships among the
norm of products of elements or vectors or functions and their quotients. Thus, we established that the norm of product of two vectors or functions is less than or equal to the norm of its quotient if the norm of the denominator is less than or equal to one. On the other hand, the norm of the quotient of two vectors or functions is less than or equal to the norm of their product is proved. In addition, we introduce the proofs of inequalities including the norm of index power of products and their quotients, and then applied these inequalities to estabish properties of some functional spaces, as well as, extend some of the results in these functional spaces.

Keywords

quotient inequalities, first quotient inequalities, second quotient inequality, index power quotient inequalities

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