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Fixed Point Theory in Locally Convex Spaces

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Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications

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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).

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Authors and Affiliations

  1. Department of Mathematics, University of Sfax, Faculty of Sciences, Sfax, Tunisia

    Afif Ben Amar

  2. School of Mathematics, National University of Ireland, Galway, Galway, Ireland

    Donal O’Regan

Authors
  1. Afif Ben Amar
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  2. Donal O’Regan
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Ben Amar, A., O’Regan, D. (2016). Fixed Point Theory in Locally Convex Spaces. In: Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-31948-3_3

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