General iterative methods for generalized equilibrium problems and fixed point problems of \(k\)-strict pseudo-contractions. (English) Zbl 1475.47080
Summary: In this paper, we modify the general iterative method to approximate a common element of the set of solutions of generalized equilibrium problems and the set of common fixed points of a finite family of \(k\)-strictly pseudo-contractive nonself mappings. Strong convergence theorems are established under some suitable conditions in a real Hilbert space, which also solves some variation inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
generalized equilibrium problem; \(k\)-strict pseudo-contractions; general iterative method; \(\alpha\)-inverse strongly monotone; common fixed point; strong convergenceReferences:
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