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

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Abstract

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.

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References

  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).

  2. 2.

    I. V. Skrypnik, Methods for Investigation of Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).

  3. 3.

    J. L. Lions, Quelques Méthodes de Résolution des Problèms aux Limites Nonlineaires, Gauthier-Villars, Paris (1969).

  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).

  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).

  6. 6.

    M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, New York (1972).

  7. 7.

    B. N. Pshenichnyi, Convex Analysis and Extremal Problems [in Russian], Nauka, Moscow (1980).

  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).

  9. 9.

    M. Z. Zgurovskii and V. S. Mel’nik, Nonlinear Analysis and Control over Infinite-Dimensional Systems [in Russian], Naukova Dumka, Kiev (1999).

  10. 10.

    J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York (1984).

  11. 11.

    H. H. Schaefer, Topological Vector Spaces, Macmillan, New York (1966).

  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).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 505–521, April, 2006.

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Mel’nik, V.S. Topological methods in the theory of operator inclusions in Banach spaces. II. Ukr Math J 58, 573–595 (2006). https://doi.org/10.1007/s11253-006-0085-6

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Keywords

  • Banach Space
  • Variational Inequality
  • Topological Vector Space
  • Topological Method
  • Reflexive Banach Space