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Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces

  • Afif Ben Amar
  • Saoussen Derbel
  • Donal O’Regan
  • Tian Xiang
Article
  • 26 Downloads

Abstract

In this paper, we establish new fixed point results for some weakly countably condensing and weakly sequentially continuous maps, fixed-point results of Krasnosel’skii–Daher type for the sum of two weakly sequentially continuous mappings in Banach spaces, a multivalued version of the Daher fixed point theorem for weakly countably condensing multimaps having w-weakly closed graph in Banach spaces and a Krasnosel’skii–Daher-type theorem for multimaps. In addition, we show the applicability of our results to the theory of Volterra integral equations in Banach spaces. Our results are formulated in terms of the axiomatic measure of weak noncompactness.

Keywords

Weakly sequentially continuous weakly countably condensing weakly countably \(1-\)set-contractive w-weakly closed graph integral equation measure of weak noncompactness 

Mathematics Subject Classification

47H09 47H10 47H30 

Notes

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Afif Ben Amar
    • 1
  • Saoussen Derbel
    • 1
  • Donal O’Regan
    • 2
  • Tian Xiang
    • 3
  1. 1.Department of Mathematics, Faculty of SciencesSfax UniversitySfaxTunisia
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  3. 3.Institute for Mathematical SciencesRenmin University of ChinaBejingPeople’s Republic of China

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