Some concepts of the biconvex sets and biconvex functions are considered in this paper. Properties of the strongly biconvex convex functions are investigated under suitable conditions. The minimum of the sum of differentiable biconvex functions and nondifferentiable biconvex functions is characterized by variational inequality, which is called mixed bivariational inequality. The auxiliary principle technique is used to propose and investigate some iterative methods along with convergence criteria. Some important special cases as applications are discussed. Results obtained in this paper can be viewed as significant refinement and improvement of previously known results.
Aslam Noor, Muhammad; Inayat Noor, Khalida; and Lotayif, Mansour
"Biconvex Functions and Mixed Bivariational Inequalities,"
Information Sciences Letters: Vol. 10
, Article 10.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss3/10