Properties of Linear Relations in Banach Spaces

  • Guojing RenEmail author
  • Ravi P. Agarwal


This paper is concerned with properties and stability of linear relations, including closed, compact, and Fredholm linear relations. Stability of closedness and compactness of linear relations under relatively bounded perturbations and relatively compact perturbations is studied. In particular, results on the stability of index of Fredholm linear relation and its iterates are discussed. The results obtained in the present paper generalize the corresponding results for single-valued linear operators to multi-valued linear operators, and some improve or relax certain assumptions of the related existing results.


Linear relation Perturbation Closedness Compactness Fredholm 

Mathematics Subject Classification

47A06 47A53 47A55 



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Authors and Affiliations

  1. 1.School of Mathematics and Quantitative EconomicsShandong University of Finance and EconomicsJinanPeople’s Republic of China
  2. 2.Department of MathematicsTexas AM University-KingsvilleKingsvilleUSA

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