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A study of normality and continuity for mixed integral equations

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Abstract

This paper presents a numerical method for solving a mixed Fredholm–Volterra linear integral equation of the second kind in a Banach space. Under certain conditions, the existence and uniqueness of the solution are proved, using Banach’s fixed point theorem. Using Nystrom’s method, the problem is reduced to a system of linear integral equations, whose solution is then found by the resolvent method. The ideas are interesting and this area caught the attention of many researchers, having so many applications. This paper starts with a brief introduction in the subject and then proposes a new scheme which is discussed in details. The numerical examples in Sect. 6 illustrate the applicability of the theoretical results.

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Acknowledgements

The authors would like to thank the referees and the editor for the valuable suggestions to improve the writing of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, 21511, Egypt

    M. A. Abdou

  2. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    M. E. Nasr & M. A. Abdel-Aty

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  1. M. A. Abdou
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  2. M. E. Nasr
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  3. M. A. Abdel-Aty
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Correspondence to M. A. Abdel-Aty.

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Abdou, M.A., Nasr, M.E. & Abdel-Aty, M.A. A study of normality and continuity for mixed integral equations. J. Fixed Point Theory Appl. 20, 5 (2018). https://doi.org/10.1007/s11784-018-0490-0

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  • DOI: https://doi.org/10.1007/s11784-018-0490-0

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