In this paper, we define and introduce some new concepts of the higher order strongly-generalized convex functions involving an arbitrary function. Some properties of the higher order strongly-generalized convex functions are investigated under suitable conditions. We have proved that the optimality conditions of higher order strongly generalized can be characterized by a class of variational inequalities, which is called higher-order strongly variational inequality. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher-order strongly-generalized affine convex functions. Results obtained in this paper can be viewed as refinement and improvement of previously-known results.
Digital Object Identifier (DOI)
Aslam Noor, Muhammad and Inayat Noor, Khalida
"Higher-Order Strongly-Generalized Convex Functions,"
Applied Mathematics & Information Sciences: Vol. 14
, Article 17.
Available at: https://dc.naturalspublishing.com/amis/vol14/iss1/17