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Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods
Authors:Verma  R. U.
Affiliation:(1) Department of Mathematics, University of Toledo, Toledo, Ohio
Abstract:Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)isinK×K such that

$$begin{gathered}  leftlangle {rho {rm T}(y^* ,x^* ) + x^*  - y^* ,x - x^* } rightrangle  geqslant 0,{text{      }}forall x in K{text{ and }}rho  > 0, hfill   leftlangle {eta {rm T}(x^* ,y^* ) + y^*  - x^* ,x - x^* } rightrangle  geqslant 0,{text{      }}forall x in K{text{ and }}eta  > 0, hfill  end{gathered}$$
where T: K×KrarrH is a nonlinear mapping on K×K.
Keywords:Relaxed cocoercive nonlinear variational inequalities  projection methods  relaxed cocoercive mappings  cocoercive mappings  convergence of projection methods
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