## Strong convergence for generalized equilibrium problems, fixed point problems and relaxed cocoercive variational inequalities.(English)Zbl 1187.47048

Summary: We introduce a new iterative scheme for finding the common element of the set of solutions of generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of variational inequality problems for a relaxed $$(u,v)$$-cocoercive and $$\xi$$-Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence to a common element of the above three sets under some suitable conditions. Our result can be considered as an improvement and refinement of previously known results.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 49J40 Variational inequalities

### Keywords:

relaxed $$(u,v)$$-cocoercive mapping; Hilbert space
Full Text:

### References:

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