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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Sfax University, LA 1171, 3000, Sfax, Tunisia

    Afif Ben Amar & Saoussen Derbel

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  3. Institute for Mathematical Sciences, Renmin University of China, Bejing, 100872, People’s Republic of China

    Tian Xiang

Authors
  1. Afif Ben Amar
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  2. Saoussen Derbel
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  3. Donal O’Regan
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  4. Tian Xiang
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Correspondence to Afif Ben Amar.

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Amar, A.B., Derbel, S., O’Regan, D. et al. Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces. J. Fixed Point Theory Appl. 21, 8 (2019). https://doi.org/10.1007/s11784-018-0644-0

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  • DOI: https://doi.org/10.1007/s11784-018-0644-0

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