## Iterative scheme for finding a common point of infinitely many convex sets in a Banach space.(English)Zbl 1071.47062

Based on previous work by Kamimura and Takahashi, and Nakajo and Takahashi, the authors study the convergence of an iterative scheme for finding a common point of a countable infinite family of closed convex subsets of a uniformly convex Banach space by using the hybrid method in mathematical programming. They prove that the sequence converges strongly to an element of the intersection set. Their results are applied to a convex minimization problem.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 90C25 Convex programming