Ukrainian Mathematical Journal

, Volume 58, Issue 4, pp 573–595 | Cite as

Topological methods in the theory of operator inclusions in Banach spaces. II

  • V. S. Mel’nik


We develop topological methods for the investigation of operator inclusions in Banach spaces, prove the generalized Ky Fan inequality, and study the critical points of many-valued mappings in topological spaces.


Banach Space Variational Inequality Topological Vector Space Topological Method Reflexive Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. S. Mel’nik, “Topological methods in the theory of operator inclusions in Banach spaces. I,” Ukr. Mat. Zh., 58, No. 2, 184–194 (2006).Google Scholar
  2. 2.
    I. V. Skrypnik, Methods for Investigation of Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).Google Scholar
  3. 3.
    J. L. Lions, Quelques Méthodes de Résolution des Problèms aux Limites Nonlineaires, Gauthier-Villars, Paris (1969).Google Scholar
  4. 4.
    V. S. Mel’nik, “Multivariational inequalities and operator inclusions in Banach spaces with mappings of the class (S)+,” Ukr. Mat. Zh., 52, No. 11, 1513–1523 (2000).MathSciNetGoogle Scholar
  5. 5.
    V. S. Mel’nik and A. N. Vakulenko, “On topological method in the theory of operator inclusions with densely defined mapping in Banach spaces,” Nonlin. Boundary Value Probl., 10, 125–142 (2000).Google Scholar
  6. 6.
    M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, New York (1972).Google Scholar
  7. 7.
    B. N. Pshenichnyi, Convex Analysis and Extremal Problems [in Russian], Nauka, Moscow (1980).Google Scholar
  8. 8.
    V. S. Mel’nik, “Generalized Ky Fan inequality and zeros of many-valued mappings,” Dopov. Nat. Akad. Nauk Ukr., No. 3, 15–19 (2004).Google Scholar
  9. 9.
    M. Z. Zgurovskii and V. S. Mel’nik, Nonlinear Analysis and Control over Infinite-Dimensional Systems [in Russian], Naukova Dumka, Kiev (1999).Google Scholar
  10. 10.
    J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York (1984).zbMATHGoogle Scholar
  11. 11.
    H. H. Schaefer, Topological Vector Spaces, Macmillan, New York (1966).Google Scholar
  12. 12.
    P. O. Kas’yanov and V. S. Mel’nyk, “On properties of subdifferential mappings in Fréchet spaces,” Ukr. Mat. Zh., 57, No. 10, 1385–1394 (2005).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. S. Mel’nik
    • 1
  1. 1.Institute of Applied System AnalysisUkrainian National Academy of Sciences and Ukrainian Ministry of Education and ScienceKiev

Personalised recommendations