For our special case, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibria problem; the minimum norm solution of the system of mixed type equilibria problem.
For the special case of our results, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibrium problem; the minimum norm solution of the system of the mixed type equilibria problem.
This point x ¯ is also a unique minimum norm common solution of fixed point and split equilibrium constraints: Find min q ∈ Fix ( T ) ∩ Ω ∥ q ∥.
The following unique minimum norm common solution of a fixed point problem and multiple sets split equilibrium problem is a special case of Theorem 4.4.
Each function of a generalized fundamental system is the unique minimum norm least squares solution of the same problem where the unique exact solution is the corresponding function of the biorthogonal fundamental system if this system exists.
A generalized Green's function is the unique minimum norm least squares solution of the problem where the unique exact solution is an ordinary Green's function if it exists.
Applying Theorems 2.2 and 4.1, Lemma 4.1, we can find the unique minimum norm common solution of fixed point and split equilibrium constraints and the solution of mathematical programming with fixed point and split equilibrium constraints.
According to what we have defined the unique unit norm vector ({{boldsymbol {tau }}_{1}} in {mathbb {C}^{N times 1}}) which lie in the null space of ({mathbf {A}}_{1}^{ast }), it also satisfies N 1 τ 1=0.
Here, it is worth mentioning, just as the SFP, that the unique minimum norm solution can be obtained through our algorithm for each of the minimization problem and the equilibrium problem by taking u = 0 in Theorems 4.8 and 4.12.
As applications, we study unique minimum norm solutions of the following problems: multiple sets split feasibility problems, system of convex constrained linear inverse problems, convex constrained linear inverse problems, split feasibility problems, convex feasibility problems.
