Abstract
Existence of solution for functional integral equations of two variables is established in this article under some weaker conditions in a Banach algebra space \(C([0, b]\times [0, b],\mathbb {R}), b>0\) in the form of two operators. We applied the concept of measure of non-compactness (in short, MNC) and Petryshyn fixed point theorem for the operators in the above-mentioned space. For applicability of the obtained results of our theorem, an interesting example is given. To compute the solution of the example, we used an iterative algorithm which was constructed by modified homotopy perturbation method and Adomian polynomials with an acceptable accuracy.
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Acknowledgements
This research is supported by Government of India CSIR JRF Fellowship, Program No. 09/1174(0003)/2017-EMR-1, New Delhi.
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Rabbani, M., Deep, A. & Deepmala On some generalized non-linear functional integral equations of two variables via measures of noncompactness and numerical method to solve it. Math Sci 15, 317–324 (2021). https://doi.org/10.1007/s40096-020-00367-0
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DOI: https://doi.org/10.1007/s40096-020-00367-0
Keywords
- Functional integral equation (FIE)
- Measure of non-compactness (in short
- MNC)
- Fixed point theorem
- Modified homotopy perturbation(MHP)