Exponential type duality for $\eta$-approximated variational problems

Abstract

In this article, we develop a new method to solve the variational problems with exponential
$(p,r)$-invex functionals. For both the considered variational problem and its original
Mond-Weir dual variational, the associated $\eta$-approximated variational problem and
its associated $\eta$-approximated Mond-Weir dual variational problem are constructed,
respectively. Then, several duality results for the considered variational problem and
its Mond-Weir dual variational problem are proved by the help of duality results established
between $\eta$-approximated variational problems mentioned above.