Existence of solutions to nonlinear functional-integral equations via the measure of noncompactness

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Abstract

The purpose of this work is to present two new notions of \(\mu \)-set contraction of a bounded subset of a Banach space and establish some fixed point and coupled fixed point results in the direction of Darbo (Rend Sem Math Univ Padova 4:84–92, 1995). We apply our work to get existence of solutions to nonlinear functional-integral equations followed by an illustration. Our work generalizes many existing results in the literature.

Keywords

Fixed point coupled fixed point measure of noncompactness functional-integral equation 

Mathematics Subject Classification

34A08 54H25 47H10 

Notes

Acknowledgements

The authors express their gratitude to the referees for careful reading of the manuscript. The first author is thankful to the United States-India Education Foundation, New Delhi, India, and IIE/CIES, Washington, DC, USA, for Fulbright-Nehru PDF Award (no. 2052/FNPDR/2015).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTexas A & M UniversityKingsvilleUSA
  2. 2.Department of MathematicsSari Branch Islamic Azad UniversitySariIran

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