Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and its dual space. Let be a bounded strongly monotone mapping such that For given let be generated by the algorithm: where J is the normalized duality mapping from E into and is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that converges strongly to the unique point Finally, our theorems are applied to the convex minimization problem.
In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators in a Banach space. We prove the strong convergence of the proposed iterative scheme without imposing any compactness condition on the mapping or the space. Finally, applications of our theorems to some constrained convex minimization problems are given.
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