Freese R.W., Yeol Je Cho. Geometry of Linear 2-Normed Spaces

New York: Nova Science Publishers, Incorporated, 2001. — 313 p.The purpose of this book is to give a comprehensive introduction to the study of 2–metric spaces and linear 2–normed spaces. Since 1963, when S. G¨ahler initially introduced the concepts of 2–metric spaces and linear 2–normed spaces, a number of authors have done considerable work on geometric structures of these spaces, for example, strict convexity, strict 2–convexity and uniform convexity, etc., and there are probably no books concerning the theory of 2–metric spaces and linear 2–normed spaces.
This book is introdued as a survey of the latest results on the relations between linear 2–normed spaces and normed linear spaces, completion of
linear 2–normed spaces, 2–inner product spaces, strict convexity, strict 2–convexity, uniform convexity, isometry conditions, orthogonal relations and
quadratic forms, etc., which are mostly due to C.R. Diminnie, R.W. Freese, R.E. Ehret, S. G¨ahler, M. Newton, Y.J. Cho, C.S. Lin and A. White, etc.,
and this compilation of results is intended as a reference work for scholars in the field and as an overview for those initiating research in this branch of
mathematics.
We hope this book will be devoted to the possible applications of metric geometry, functional analysis and topology, as a new tool.