In the absence of restrictions on which mappings are acceptable, such mappings are relatively easy to come by.
Importantly, we employed a task in which stimulus response outcome mappings were deterministic (in contrast to most reversal paradigms where mappings are probabilistic), such that unexpected outcomes triggered a switch in response set rather than new learning, which is also dopamine-dependent.
Remark 2.4 We point out that the order in which the mappings in condition (b) of Theorem 2.3 are considered is crucial.
It is observed that there are many situations in which the mappings are not contractive on the whole space but they may be contractive on its subsets.
By constrasting with other methods, our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined.
Compared with the relaxed extragradient method in [[8], Theorem 3.2], our relaxed viscosity iterative algorithms (i.e., Algorithms 3.1 and 3.2) drop the requirement of boundedness for the domain in which various mappings are defined.
In our strong convergence results, the relaxed and hybrid viscosity iterative algorithms drop the requirement of boundedness for the domain in which various mappings are defined; see, e.g., Yao et al. [[8], Theorem 3.2].
Compared with the relaxed extragradient iterative algorithm in [[8], Theorem 3.2], our hybrid viscosity iterative algorithms (i.e., Algorithms 4.1 and 4.2) remove the requirement of boundedness for the domain C in which various mappings are defined.
The cost of the best solution is then compared with costs found in reconciliations in which tip mappings are permuted at random.
We next briefly review some literatures in which the involved mappings and are all nonexpansive.
