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Introduction This work is motivated as an attempt to deal with an estimation of the relative error for the eigenvalues of the Sturm-Liouville problem. We are interested in finding upper bounds for such error. The uniform spectral continuity of this operator was treated in  in very simple manner. It is worth pointing out that the knowledge of the bounds for these two errors allows us to consider the eigenvalue problem for Sturm-Liouville operator in normal form to be perfectly posed for eachdoi:10.1515/dema-1999-0213 fatcat:uy6pg44evjesng4op6cahage4q