N-NORMED SPACES AND CONTRACTIVE MAPPING THEOREM

• Main Author: EKARIANI (30112001), SHELVI
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/24286
• Institution: Institut Teknologi Bandung

This dissertation discusses n-normed spaces and contractive mapping theorem. An n- normed space is a vector space equipped by an n-norm. Geometrically, an n-norm is a measure of paralelepipedum’s volume that was spanned by n vectors. Conceptually, it is a generalization of a norm. An n-norm can be defined on a normed space and a norm can also be defined on an n-normed space. Related to these facts, this dissertation gives a different way of looking at n-normed spaces by studying the connection between the n-norm and the norm that was induced by it. Some topological concepts in an n-normed space, such as sequences and completeness, may be developed from related concepts that already exist in normed spaces. <br /> <br /> <br /> <br /> <br /> The second section in this dissertation is to examine the contractive mapping theorem in both complete finite dimensional n-normed spaces and complete infinite dimensional n-normed spaces. In 2001, Gunawan formulated a fixed point theorem in some n-normed spaces. This theorem was proved by using the induced norm and the fixed point theorem on normed spaces. However, Gunawan’s theorem requires the conditions that are too strict in ensuring the existence of the fixed point. As a refinement of the theorem, this dissertation formulates a contractive mapping theorem with simpler conditions than the conditions that was given by Gunawan.