Strong convergence theorems for mixed equilibrium problem and asymptotically \(I\)-nonexpansive mapping in Banach spaces. (English) Zbl 1473.47034
Summary: This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
hybrid algorithm; fixed point problem; asymptotically nonexpansive mappings; uniformly smooth Banach space; strong convergenceReferences:
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