Duality of variational problems with a new approach

Abstract

The present investigation introduces the third order duality in variational problems, as because, in certain situations, first and second order duality do not yield solutions but it succeeds in finding the desired results. The duality results for the pair of variational primal problems and their corresponding third order dual problems are demonstrated. Counterexamples are provided to justify the importance of the current research work. It is found that many reported results of the literature are particular cases of this paper.