In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point...

Given non-empty subsets A and B of a metric space, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S{:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${T {:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> be non-self mappings. Due to the fact that S and T are non-self mappings, the equations Sx=x and Tx=x are likely to have no common solution, known as a common fixed point...</equationsource></inlineequation></equationsource></inlineequation>

Let us suppose that A and B are nonempty subsets of a metric space. Let S:A⟶B and T:A⟶B be nonself-mappings. Considering the fact S and T are nonself-mappings, it is feasible that the equations Sx=x and Tx=x have no common solution, designated as a common fixed point of the mappings S and T....

In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point...