The question we address is whether X carries a unique invariant norm in the sense that ||·|| is the unique norm on X for which τ is a representation.
Each place I have called home has its unique cultural norms and values that influence every aspect of life, from how we interact with strangers, to how we build a social life, to how we conduct business.
Illuminating these underlying factors and how they relate to service use may help clinicians and planners determine if and how services should be targeted to meet the unique needs, norms, attitudes and knowledge of diverse immigrants in a multi-cultural context like Ontario, Canada.
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 ∥.
As a direct consequence, we obtain the unique minimum-norm common point of the solution set and the fixed point set.
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.
When a special kind of initial iteration matrix group is chosen, the unique least-norm generalized reflexive solution of the general coupled matrix equations can be derived.
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.
