Abstract
This work manifests the credibility of Darbo’s fixed point theory towards the solvability of nonlinear functional convolution integral equation with deviating argument. The solution space is taken to be the space of Lebesgue integrable functions defined on \(\mathbb {R_+}\). The concept of measure of noncompactness in correlation with the compactness criterion, i.e., Kolmogorov–Riesz compactness theorem in \(L^{p}(\mathbb {R_+})\) space has been taken. Then under certain suitable hypotheses and by the assistance of Darbo’s fixed point theory, sufficient conditions for the existence of the solution have been introduced. Finally, some examples have been taken to justify the result.
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Saha, D., Sen, M., Roy, S. (2021). Investigation of the Existence Criteria for the Solution of the Functional Integral Equation in the \(L^{p}\) Space. In: Chadli, O., Das, S., Mohapatra, R.N., Swaminathan, A. (eds) Mathematical Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 381. Springer, Singapore. https://doi.org/10.1007/978-981-16-8177-6_16
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DOI: https://doi.org/10.1007/978-981-16-8177-6_16
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