Topological Vector-Space Valued Cone Banach Spaces

Mehmood, Nayyar; Azam, Akbar; Aleksic, Suzana

Research Article

Topological Vector-Space Valued Cone Banach Spaces

Nayyar Mehmood¹*
Akbar Azam¹
Suzana Aleksic²

COMSATS Institute of Information Technology, Park road, Islamabad, Pakistan.
Faculty of Science, University of Kragujevac, Radoja Domanovića 12, 34 000 Kragujevac, Serbia

* Corresponding author

Abstract

In this paper we introduce the notion of tvs-cone normed spaces, discuss related topological concepts and characterize the tvs-cone norm in various directions. We construct generalize locally convex tvs generated by a family of tvs-cone seminorms. The class of weak contractions properly includes large classes of highly applicable contractions like Banach, Kannan, Chatterjea and quasi etc. We prove fixed point results in tvs-cone Banach spaces for nonexpansive self mappings and self/non-self weak contractive mappings. We discuss the necessary conditions for T -stability of Picard iteration. To ensure the novelty of our work we establish an application in homotopy theory without the assumption of normality on cone and many non-trivial examples.

How to Cite

N. Mehmood, A. Azam, S. Aleksic, Topological Vector-Space Valued Cone Banach Spaces, Int. J. Anal. Appl. 6 (2014), 205–219.

BibTeX

@article{Mehmood2014,
  author  = {Mehmood, Nayyar and Azam, Akbar and Aleksic, Suzana},
  title   = {Topological Vector-Space Valued Cone Banach Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {6},
  year    = {2014},
  pages   = {205--219},
  doi     = {}
}

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