Advertisement

Positivity

, Volume 19, Issue 2, pp 333–340 | Cite as

On fixed point theorems for monotone increasing vector valued mappings via scalarizing

  • P. Zangenehmehr
  • A. P. FarajzadehEmail author
  • S. M. Vaezpour
Article

Abstract

In this paper, first we prove some lemma, then by using the nonlinear scalarization mapping, we present some fixed point theorems for a vector valued mapping. The main result obtained can be viewed as an extension, improvement and repairment of the main theorem given in Kostrykin and Oleynik (Fixed Point Theory Appl 2012:211, 2012).

Keywords

Fixed point Nonlinear scalarization mapping Solid cone  Minihedral cone Vector valued mapping Partially ordered 

Mathematics Subject Classification

46.005 47.025 47.040 

References

  1. 1.
    Abdeljawad, T.: Order norm completions of cone metric spaces. Numer. Funct. Anal. Optim. 32(5), 477–495 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Arandelovic, I.D. Keckic, D.J.: TVS-cone metric spaces as a special case of metric spaces. arXiv:1202.5930vl [math.FA] (2012)
  3. 3.
    Chen, G.Y., Yang, X.Q., Yu, H.: A nonlinear scalarization function and generalized quasi-vector equilibrium. J. Glob. Optim. 32, 451–466 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)zbMATHCrossRefGoogle Scholar
  5. 5.
    Du, W.S.: A note on cone metric fixed point theory and its equivalence. Nonlinear Anal. 72(5), 2259–2261 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Gerstewitz (Tammer), Chr.: Nichtkonvexe Dualitt in derVektoroptimierung. Wiss. Zeitschr. TH Leuna-Mersebg. 25, 357–364 (1983)Google Scholar
  7. 7.
    Gerstewitz (Tammer), Chr., Weinder, P.: Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67(2), 297–320 (1990)Google Scholar
  8. 8.
    Khamsi, M.A., Kirkan, W.A.: Introduction to Metric Spaces and Fixed Point Theory. Wiley, New York (2007)Google Scholar
  9. 9.
    Kostrykin, V., Oleynik, A.: An intermediate value theorem for monotone operators in ordered Banach spaces. Fixed Point Theory Appl. 2012, 211 (2012)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kostrykin, V., Oleynik, A.: On the existence of unstable bumps in neural networks, Preprint. arXiv:1112.2941 [math.Ds] (2011)

Copyright information

© Springer Basel 2014

Authors and Affiliations

  • P. Zangenehmehr
    • 1
  • A. P. Farajzadeh
    • 2
    Email author
  • S. M. Vaezpour
    • 3
  1. 1.Department of Mathematics Science and Research BranchIslamic Azad universityTehranIran
  2. 2.Department of MathematicsRazi UniversityKermanshahIran
  3. 3.Department of MathematicsAmirkabir University of TechnologyTehranIran

Personalised recommendations