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Fixed Point Theorems for Multi-valued Nonexpansive Mappings in Banach Spaces

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Abstract

In this paper, we present new fixed point theorems for multivalued nonexpansive mappings. Since Banach space can have any geometric structure, we consider mappings such that their perturbation by the identity operator is expansive. Then we derive some fixed point results including existence theorems for the sum and product of some classes of nonlinear operators. Three illustrating examples for functional and differential inclusions are supplied.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her careful reading of the original manuscript which led to substantial improvement of the paper.

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Authors and Affiliations

  1. Laboratoire “Théorie du Point Fixe et Applications” ENS, ENS, Kouba, BP 92, 16016, Algiers, Algeria

    Zineb Bounegab & Smaïl Djebali

  2. Al Imam Mohammad Ibn Saud Islamic University (IMSIU), PB 90950, Riyadh, 11623, Saudi Arabia

    Smaïl Djebali

Authors
  1. Zineb Bounegab
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  2. Smaïl Djebali
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Correspondence to Smaïl Djebali.

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Bounegab, Z., Djebali, S. Fixed Point Theorems for Multi-valued Nonexpansive Mappings in Banach Spaces. Mediterr. J. Math. 16, 49 (2019). https://doi.org/10.1007/s00009-019-1327-9

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  • DOI: https://doi.org/10.1007/s00009-019-1327-9

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