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An extension of Sadovskii’s fixed-point theorem with applications to integral equations


In this paper, we give a generalization of Sadovski\(\breve{\text {i}}\)’s fixed-point theorem for condensing operators, which is slightly more flexible than this result in applying to some different problems. We apply our extension to prove some results in integral equations. At the end, we illustrate our results by concrete examples to confirm that our method can be used effectively to solve some integral equations.

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The author would like to thank Mahabad Branch, Islamic Azad University for the financial support of this study, which is based on a research with project code: 51663931110002.

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Correspondence to Hassan Khandani.

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This work was completed with the support of Islamic Azad university of Mahabad.

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Khandani, H. An extension of Sadovskii’s fixed-point theorem with applications to integral equations. J. Fixed Point Theory Appl. 20, 15 (2018).

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  • Integral equations
  • Measure of noncompactness
  • Kuratowski measure of noncompactness
  • Condensing operators
  • Sadovski\(\breve{\text {i}}\) fixed-point theorem

Mathematics Subject Classification

  • Primary 47H08
  • Secondary 47H10