On a class of inverse Sturm–Liouville problems with eigenparameter-dependent boundary conditions

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A class of inverse Sturm–Liouville problems of Atkinson type with eigenparameter-dependent boundary conditions is investigated. By using the matrix representations of the Sturm–Liouville problems with eigenparameter-dependent boundary conditions and a special class of inverse matrix eigenvalue problems, the corresponding Sturm–Liouville problems are constructed by using two sets of interlacing real numbers satisfying certain conditions. An algorithm and some examples are also given to illustrate our results.