Skip to main content
Log in

Demicompact and k-D-Set-contractive Multivalued Linear Operators

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we extend the concept of demicompactness and k-set-contractive linear operators on multivalued linear operators and we develop some properties. Finally, we establish a rapport with the theory of fixed points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alvarez, T.: On almost semi-Fredholm linear relations in normed spaces. Glasg. Math. J. 47(1), 187–193 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alvarez, T.: Linear relations on hereditarily indecomposable normed spaces. Bull. Aust. Math. Soc. 84(1), 49–52 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Alvarez, T., Cross, R.W., Wilcox, D.: Multivalued Fredholm type operators with abstract generalised inverses. J. Math. Anal. Appl. 261(1), 403–417 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Alvarez, T., Ammar, A., Jeribi, A.: On the essential spectra of some matrix of linear relations. Math. Methods Appl. Sci. 37(5), 620–644 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ammar, A.: A characterization of some subsets of essential spectra of a multivalued linear operator. Complex Anal. Oper. Theory 11(1), 175–196 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Arens, R.: Operational calculus of linear relations. Pac. J. Math. 11, 9–23 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  7. Artstein, Z.: Continuous dependence of solutions of operator equations. I. Trans. Am. Math. Soc. 231(1), 143–166 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ayerbe Toledano, J.M., Dominguez Benavides, T., López Acedo, G.: Measures of Noncompactness in Metric Fixed Point Theory. Operator Theory: Advances and Applications, vol. 99. Birkhäuser, Basel (1997)

    Book  MATH  Google Scholar 

  9. Chaker, W., Jeribi, A., Krichen, B.: Demicompact linear operators, essential spectrum and some perturbation results. Math. Nachr. 288(13), 1476–1486 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Coddington, E.A.: Extension Theory of Formally Normal and Symmetric Subspaces. Memoirs of the American Mathematical Society, vol. 134. American Mathematical Society, Providence (1973)

  11. Cross, R.W.: Multivalued Linear Operators. Monographs and Textbooks in Pure and Applied Mathematics, vol. 213. Marcel Dekker, New York (1998)

    Google Scholar 

  12. Darbo, G.: Punti uniti in transformazioni a condominio non compatto. Rend. Sem. Mat. Univ. Padova 24, 84–92 (1955)

    MathSciNet  MATH  Google Scholar 

  13. Jeribi, A.: Spectral Theory and Applications of Linear Operators and Block Operator Matrices. Springer, New York (2015)

    Book  MATH  Google Scholar 

  14. Jeribi, A.: Linear Operators and Their Essential Pseudospectra. CRC Press, Boca Raton (2018)

    MATH  Google Scholar 

  15. Kuratowsci, K.: Topology, vol. 1, new edition. Panstwowe Wydawnictwo Naukowe, Warsaw (1966)

  16. Krichen, B.: Relative essential spectra involving relative demicompact unbounded linear operators. Acta Math. Sci. Ser. B Engl. Ed. 34(2), 546–556 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nussbaum, R.D.: The fixed point index and fixed point theorems for k-set-contractions, Ph.D. Thesis. The University of Chicago, ProQuest LLC, Ann Arbor (1969)

  18. Opial, Z.: Nonexpansive and monotone mappings in Banach spaces. Brown Univ Providence Ri Center For Dynamical Systems, no. CDS-LN-67-1 (1967)

  19. Petryshyn, W.V.: Construction of fixed points of demicompact mappings in Hilbert space. J. Math. Anal. Appl. 14, 276–284 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  20. Petryshyn, W.V.: Remarks on condensing and \(k\) -set-contractive mappings. J. Math. Anal. Appl. 39, 717–741 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wilcox, D.: Multivalued semi-Fredholm operators in normed linear spaces, Ph.D. Diss. Thesis. University of Cape Town (2002)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aref Jeribi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ammar, A., Daoud, H. & Jeribi, A. Demicompact and k-D-Set-contractive Multivalued Linear Operators. Mediterr. J. Math. 15, 41 (2018). https://doi.org/10.1007/s00009-018-1078-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-018-1078-z

Keywords

Mathematics Subject Classification

Navigation