Normed proper quasilinear spaces


ÇAKAN S., YILMAZ Y.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, vol.8, no.5, pp.816-836, 2015 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.22436/jnsa.008.05.32
  • Journal Name: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.816-836

Abstract

The fundamental deficiency in the theory of quasilinear spaces, introduced by Aseev [S. M. Aseev, Trudy Mat. Inst. Steklov., 167 (1985), 25-52], is the lack of a satisfactory definition of linear dependence-independence and basis notions. Perhaps, this is the most important obstacle in the progress of normed quasilinear spaces. In this work, after giving the notions of quasilinear dependence-independence and basis presented by Banazili[H. K. Banazili, M. Sc. Thesis, Malatya, Turkey (2014)] and Cakan [S. Cakan, Ph.D. Seminar, Malatya, Turkey (2012)], we introduce the concepts of regular and singular dimension of a quasilinear space. Also, we present a new notion namely "proper quasilinear spaces" and show that these two kind dimensions are equivalent in proper quasilinear spaces. Moreover, we try to explore some properties of finite regular and singular dimensional normed quasilinear spaces. We also obtain some results about the advantages of features of proper quasilinear spaces. (C) 2015 All rights reserved.