Abstract
In this survey paper error estimates of approximations in complex domain for the Laplace and Mellin transform are given for functions f which vanish beyond a finite domain \(\left [ a,b\right ] \subset \left [ 0,\infty \right \rangle \) and whose derivative belongs to \(L_{p}\left [ a,b \right ] \). New inequalities involving integral transform of f, integral mean of f and exponential and logarithmic mean of the endpoints of the domain of f are presented. These estimates enable us to obtain two associated numerical quadrature rules for each transform and error bounds of their remainders.
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References
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Aljinović, A.A. (2019). Error Estimates of Approximations for the Complex Valued Integral Transforms. In: Andrica, D., Rassias, T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham. https://doi.org/10.1007/978-3-030-27407-8_2
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DOI: https://doi.org/10.1007/978-3-030-27407-8_2
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