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A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

  • Mehdi Asadi
  • Moosa GabelehEmail author
  • Calogero Vetro
Article
  • 45 Downloads

Abstract

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

Keywords

Fixed point measure of noncompactness simulation function integral equation 

Mathematics Subject Classification

Primary 47H08 Secondary 54H25 

Notes

Acknowledgements

The authors wish to thank the expert referee for his/her corrections and remarks.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsZanjan Branch Islamic Azad UniversityZanjanIran
  2. 2.Department of MathematicsAyatollah Boroujerdi UniversityBorujerdIran
  3. 3.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly

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