Biconvex Functions and Mixed Bivariational Inequalities

Authors

Muhammad Aslam Noor, Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanFollow
Khalida Inayat Noor, Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanFollow
Mansour Lotayif, College of Administrative Sciences, Applied Science University, P.O. Box 5055, East Al-Ekir, Kingdom of BahrainFollow

Abstract

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.

Recommended Citation

Aslam Noor, Muhammad; Inayat Noor, Khalida; and Lotayif, Mansour (2021) "Biconvex Functions and Mixed Bivariational Inequalities," Information Sciences Letters: Vol. 10 : Iss. 3 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss3/10