## Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces.(English)Zbl 1170.47049

Summary: We introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then we study the strong and weak convergence of the sequences.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics 49J40 Variational inequalities
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### References:

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