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Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application

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  • Mohamed Amine Farid
  • El Miloudi Marhrani
  • Mohamed Aamri
  • Huseyin Isik

Abstract

In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2×2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.

Suggested Citation

  • Mohamed Amine Farid & El Miloudi Marhrani & Mohamed Aamri & Huseyin Isik, 2021. "Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, July.
    • Handle: RePEc:hin:jjmath:9985817
    DOI: 10.1155/2021/9985817
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