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Fixed Point Theory in Locally Convex Spaces

In: Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications

Author

Listed:
  • Afif Ben Amar

    (University of Sfax, Faculty of Sciences, Department of Mathematics)

  • Donal O’Regan

    (National University of Ireland, Galway, School of Mathematics)

Abstract

In this section we discuss the existence of fixed points for weakly sequentially continuous mappings on domains of Banach spaces. We first present some applicable Leray–Schauder type theorems for weakly condensing and 1-set weakly contractive operators. The main condition is formulated in terms of De Blasi’s measure of weak noncompactness β (see Sect. 1.12).

Suggested Citation

  • Afif Ben Amar & Donal O’Regan, 2016. "Fixed Point Theory in Locally Convex Spaces," Springer Books, in: Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications, chapter 0, pages 45-83, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31948-3_3
    DOI: 10.1007/978-3-319-31948-3_3
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