Common solution for a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

“…From the diversity of nonlinear problems that were solved in connection with the class of demicontractive mappings, we shall expose in more details only two of them, namely, the variational inequality problems and equilibrium problems. For other problems, namely for minimization problems, we refer to Arfat et al [31] and Chang et al [101].…”

“…We end this section by mentioning another important application of the above results to convex minimization over the fixed-point set of demicontractive mappings (a topic which is not reviewed here); see Maingé [21], Mewomo [128], Okeke et al [109], Chang et al [101], Jailoka et al [129], Arfat et al [31], etc.…”

"A modified Halpern extragradient method for equilibrium and fixed point problems in CAT(0) space"

“…Under certain assumption, weak convergence of the sequence {x n } generated by (1.2) to a solution of some equilibrium problem has been established. In recent time, several authors have extended the notion of equilibrium to Hadamard spaces, see for example [8,11,12,25,26].…”