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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

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Zanjan Branch Islamic Azad University, Zanjan, Iran

    Mehdi Asadi

  2. Department of Mathematics, Ayatollah Boroujerdi University, Borujerd, Iran

    Moosa Gabeleh

  3. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

Authors
  1. Mehdi Asadi
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  2. Moosa Gabeleh
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  3. Calogero Vetro
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Correspondence to Moosa Gabeleh.

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Asadi, M., Gabeleh, M. & Vetro, C. A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations. Results Math 74, 86 (2019). https://doi.org/10.1007/s00025-019-1010-2

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