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.
Similar content being viewed by others
References
Alvarez, T.: On almost semi-Fredholm linear relations in normed spaces. Glasg. Math. J. 47(1), 187–193 (2005)
Alvarez, T.: Linear relations on hereditarily indecomposable normed spaces. Bull. Aust. Math. Soc. 84(1), 49–52 (2011)
Alvarez, T., Cross, R.W., Wilcox, D.: Multivalued Fredholm type operators with abstract generalised inverses. J. Math. Anal. Appl. 261(1), 403–417 (2001)
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)
Ammar, A.: A characterization of some subsets of essential spectra of a multivalued linear operator. Complex Anal. Oper. Theory 11(1), 175–196 (2017)
Arens, R.: Operational calculus of linear relations. Pac. J. Math. 11, 9–23 (1961)
Artstein, Z.: Continuous dependence of solutions of operator equations. I. Trans. Am. Math. Soc. 231(1), 143–166 (1977)
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)
Chaker, W., Jeribi, A., Krichen, B.: Demicompact linear operators, essential spectrum and some perturbation results. Math. Nachr. 288(13), 1476–1486 (2015)
Coddington, E.A.: Extension Theory of Formally Normal and Symmetric Subspaces. Memoirs of the American Mathematical Society, vol. 134. American Mathematical Society, Providence (1973)
Cross, R.W.: Multivalued Linear Operators. Monographs and Textbooks in Pure and Applied Mathematics, vol. 213. Marcel Dekker, New York (1998)
Darbo, G.: Punti uniti in transformazioni a condominio non compatto. Rend. Sem. Mat. Univ. Padova 24, 84–92 (1955)
Jeribi, A.: Spectral Theory and Applications of Linear Operators and Block Operator Matrices. Springer, New York (2015)
Jeribi, A.: Linear Operators and Their Essential Pseudospectra. CRC Press, Boca Raton (2018)
Kuratowsci, K.: Topology, vol. 1, new edition. Panstwowe Wydawnictwo Naukowe, Warsaw (1966)
Krichen, B.: Relative essential spectra involving relative demicompact unbounded linear operators. Acta Math. Sci. Ser. B Engl. Ed. 34(2), 546–556 (2014)
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)
Opial, Z.: Nonexpansive and monotone mappings in Banach spaces. Brown Univ Providence Ri Center For Dynamical Systems, no. CDS-LN-67-1 (1967)
Petryshyn, W.V.: Construction of fixed points of demicompact mappings in Hilbert space. J. Math. Anal. Appl. 14, 276–284 (1966)
Petryshyn, W.V.: Remarks on condensing and \(k\) -set-contractive mappings. J. Math. Anal. Appl. 39, 717–741 (1972)
Wilcox, D.: Multivalued semi-Fredholm operators in normed linear spaces, Ph.D. Diss. Thesis. University of Cape Town (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-018-1078-z
Keywords
- Linear relation
- multivalued linear operator
- demicompact
- semi-Fredholm relation
- k-D-set-contractive
- D-set-condensing
- fixed point