## Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings.(English)Zbl 1187.47054

Summary: We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpansive mapping in a Banach space.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics 65J15 Numerical solutions to equations with nonlinear operators
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### References:

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