Mansour and Riahi [12] proved the Hölder continuity of the unique solution for a parametric equilibrium problem under the concepts of strong monotonicity and Hölder continuity.
In fact, Chang et al. [20], Verma [33], Huang and Noor [47], Noor and Noor [28] studied the convergence analysis of the proposed iterative algorithms under the condition of strong monotonicity.
We observe that the semicontinuity of solution maps for the PVEP has been discussed under the assumption of C-strict (strong) monotonicity, which implies that the f-solution set of the PVEP is a singleton for a linear continuous functional f (see [5, 7, 8, 10, 11]).
Using the uniformly strong monotonicity of, we can obtain the following existence result for SVI under the condition that is a nonempty closed and convex subset of.
Note that cocoercivity is a weaker condition than strong monotonicity.
The strong monotonicity condition guarantees the uniqueness of the solution.
(2) When ℬ = ℋ, (i - iv) of Defi - ivn 2.1 reduce tofthe Definitions of monotonicity, strict monotonicity, strong monotonicity, and strong monotonicity with respect to A, respectively (see [3, 18]). .
When ℬ = ℋ, (i - iv) of Defi - ivn 2.1 reduce tofthe Definitions of monotonicity, strict monotonicity, strong monotonicity, and strong monotonicity with respect to A, respectively (see [3, 18]).
However, the convergence analysis does require some sort of strong monotonicity besides the Lipschitz continuity.
The strong monotonicity of F implies that and the uniqueness is proved.
