Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast approximate solution methods. One promi
Recently, Huang and Li [J. Li, N.J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006) 464–471] introduced and studied a new class of vector F-implicit complementarity problems and vector F-implicit variational inequality problems in B
In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We also derive some new
and Applied Analysis 3 set of a nonexpansive mapping in a Hilbert space. Let an arbitrary x1 ∈ H, define sequences {xn} and {un} by F ( un, y ) 1 βn 〈 y − un, un − xn 〉 ≥ 0, ∀y ∈ C, xn 1 αnγf xn I − αnB Sun, ∀n ∈ N. 1.6 They proved that under certain appropriate conditions impose