General nonconvex variational inclusions and fixed point problems

Narin Petrot, Javad Balooee
2013 Journal of Inequalities and Applications  
In this paper, we introduce and study a new system of general nonconvex variational inclusions involving four different nonlinear operators (SGNVI) and prove the equivalence between the SGNVI and a fixed point problem. By using this equivalent formulation, we establish the existence and uniqueness theorem for solution of the SGNVI. We use the foregoing equivalent alternative formulation and two nearly uniformly Lipschitzian mappings S 1 and S 2 to suggest and analyze some new two-step
more » ... two-step projection iterative algorithms for finding an element of the set of fixed points of the nearly uniformly Lipschitzian mapping Q = (S 1 , S 2 ), which is the unique solution of the SGNVI. Further, the convergence analysis of the suggested iterative algorithms under suitable conditions is studied. MSC: Primary 47H05; secondary 47J20; 49J40; 90C33
doi:10.1186/1029-242x-2013-377 fatcat:dntix5zuvraf3aq4a5h2oiqiwy