In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

In this paper, the second regularized trace formula for the differential operator with antiperiodic boundary conditions is obtained.

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We obtain absolute Tauberian constants for the H-J generalized Hausdorff transformations. As corollaries we obtain the analogous results for the E-J generalized Hausdorff matrices, and the results of Sherif for regular Hausdorff matrices.

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