N-NORMED SPACES WITH RESPECT TO ITS QUOTIENT SPACES

• Main Author: Batkunde, Harmanus
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/51053
• Institution: Institut Teknologi Bandung

The concept of n-normed spaces, for n 2 is a generalization of the concept of normed spaces. The structure of n-normed spaces has been studied since S. G¨ahler introduced the concept on 1960’s. This disertation contains some results about charactheristics of n-normed spaces with respect to norms that is derived from n-norm on its quotient spaces. These norms will be a new viewpoint to investigate some characterisics of n-normed spaces. Some topological properties of the n-normed spaces haas been studied in this research. Moreover, the number of norms that are used to investigate the topological properties become one of our concern. Therefore, we give a condition to minimize the number of norms that can be used to investigate the properties. We use the norms on the quotient spaces to study continuous and contractive functions in n-normed spaces. By using some properties that has been studied earlier, we proved Fixed Point Theorem of contractive mappings on closed and bounded sets in the n-normed spaces. We also proved Fixed Point Theorem on p-summable sequence space (`p) as one of n-normed spaces. In the end of this disertation, this research focused on bounded linear functionals and bounded k-linear functionals with their dual spaces respectively.