Affiliation:
1. Mathematics Department, COMSATS University Islamabad, Islamabad, Pakistan
Abstract
In this paper, we consider a new system of absolute value variational inclusions. Some interesting and extensively problems such as absolute value equations, difference of monotone operators, absolute value complementarity problem and hemivariational inequalities as special case. It is shown that variational inclusions are equivalent to the fixed point problems. This alternative formulation is used to study the existence of a solution of the system of absolute value inclusions. New iterative methods are suggested and investigated using the resolvent equations, dynamical system and nonexpansive mappings techniques. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results.
Reference51 articles.
1. F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space, SIAM J. Optim. 14 (2003), 773-782. https://doi.org/10.1137/S1052623403427859
2. R. W. Cottle, J.-S. Pang and R. E. Stone, The Linear Complementarity Problem, SIAM Publ., 2009.
3. S. Batool, M. Aslam Noor and K. Inayat Noor, Absolute value variational inequalities and dynamical systems, Inter. J. Anal. Appl. 18(3) (2020), 337-355.
4. S. Batool, M. Aslam Noor and K. Inayat Noor, Merit functions for absolute value variational inequalities, AIMS Math. 6(11) (2021), 12133-12147. https://doi.org/10.3934/math.2021704
5. P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Annals Oper. Research 44 (1993), 7-42. https://doi.org/10.1007/BF02073589
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献