Vol. 40, No. 2, 1972

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A new type of variational theory sufficiency theorem

Russell Daniel Rupp, Jr.

Vol. 40 (1972), No. 2, 415–444

This paper contains a sufficiency theorem appropriate to applications of Hestenes’ method of multipliers. It is a generalization of the lemma of Hahn, which has been used by previous authors to prove variable end point sufficiency theorems. The classical and control formulations of the problems of Mayer, Lagrange, and Bolza in both parametric and nonparametric form are included. The method of proof is indirect.

Mathematical Subject Classification
Primary: 49B05
Received: 4 December 1970
Published: 1 February 1972
Russell Daniel Rupp, Jr.