We first establish the equivalence between the system of general nonlinear regularized nonconvex variational inequalities and fixed point problems and, by the equivalent formulation, we discuss the existence and uniqueness of solution of the proposed system.
By using the equivalent formulation, the existence and uniqueness theorems for solutions of the system are established.
Thus, we have the equivalent formulation.
This leads to the equivalent formulation u ( k + log a, t ) = 1 2 π ∫ − ∞ ∞ f ˆ h ( a ω ) e i ω t d ω. (12).
Then, we use two nearly uniformly Lipschitzian mappings S 1 and S 2 and the equivalent alternative formulation (3.5) to suggest and analyze some new two-step projection iterative algorithms for finding an element of the set of fixed points Q = ( S 1, S 2 ), which is the unique solution of SGNVI (3.1).
We first verify the equivalence between the SGNMVID and the fixed point problems, and then by this equivalent formulation, we discuss the existence and uniqueness of the solution of the SGNMVID.
For a given rate r(t), this equation for Ψ is easily solved and it gives the following equivalent formulation: (5) Ψ (t ) = exp - ∫ 0 t r (t ′ ) d t ′, being Ψ 0) = P r{ τ >0} = 1.
In this article, we use the following equivalent formulation (see [18] WCS X = inf lim n, m ; n ≠ m x n - x m.
But instead, we find the following equivalent formulation as a maximization problem more useful since it naturally gives rise to a measure of factorizability.
In our work [21], we clearly derive a sequence of a dozen statements which characterize the KKM spaces and equivalent formulations of the partial KKM principle.
In this section, applying nearly uniformly Lipschitzian mappings S i ( i = 1, 2, 3 ) and by using the equivalent alternative formulation (3.1), we suggest and analyze some new three-step resolvent iterative algorithms with mixed errors for finding an element of the set of fixed points of Q = ( S 1, S 2, S 3 ), which is the unique solution of SGNMVID (2.1).
