In this paper, we prove that the optimality conditions of the higher order strongly convex functions are characterized by a class of variational inequalities, which is called the higher order strongly variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving higher order strongly variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.
Aslam Noor, Muhammad; Inayat Noor, Khalida; and M. Y. Al-Bayatti, Hilal
"Higher Order Variational Inequalities,"
Information Sciences Letters: Vol. 11
, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss1/1