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Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in \(\ell _{p}\left( 1<p< \infty \right) \)

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Abstract

In this article, we establish the existence of solution of infinite systems of integral equations in two variables in the sequence space \(\ell _{p}(1<p<\infty )\) by using Meir–Keeler condensing operators. We explain the results with the help of simple examples.

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Acknowledgements

The authors would like to thank Prof. Manuel López-Pellicer, Editor in Chief and the referees for his/her much encouragement, constructive criticism, careful reading and making a useful comment which improved the presentation and the readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, 791112, India

    Anupam Das & Bipan Hazarika

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, 781014, India

    Bipan Hazarika

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    M. Mursaleen

Authors
  1. Anupam Das
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  2. Bipan Hazarika
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  3. M. Mursaleen
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Correspondence to Bipan Hazarika.

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Das, A., Hazarika, B. & Mursaleen, M. Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in \(\ell _{p}\left( 1<p< \infty \right) \). RACSAM 113, 31–40 (2019). https://doi.org/10.1007/s13398-017-0452-1

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  • DOI: https://doi.org/10.1007/s13398-017-0452-1

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