The behaviour of measures of noncompactness in \(L^\infty ({\mathbb {R}}^n)\) with application to the solvability of functional integral equations

  • Reza Allahyari
Original Paper


In this work, we define a new measure of noncompactness on the space \(L^\infty ({\mathbb {R}}^n)\). In addition, we study the existence of solutions for a class of nonlinear functional integral equations of Fredholm type by using an extension of Darbo’s fixed point theorem associated with this new measure of noncompactness. Also, we will include an example which shows the efficiency of our results. The obtained results improve several ones obtained earlier.


Measure of noncompactness Darbo’s fixed point theorem Fixed point Modulus of continuity Integral equations 

Mathematics Subject Classification

47H09 47H10 


Compliance with ethical standards

Conflict of interest

The author declares that they have no competing interests.


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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Mashhad BranchIslamic Azad UniversityMashhadIran

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