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Volume 1, Issue 1, 1 April 2017, Pages 1-23
Abstract. In this paper, using a new class of nonlinear mappings called demimetric, we first prove a weak convergence theorem by the Mann type iteration for finding a common element of the set of common fixed points of an infinite family of these new demimetric mappings and the set of common solutions of variational inequality problems for an infinite family of inverse strongly monotone mappings in a Hilbert space. Furthermore, we prove a strong convergence theorem by the Halpern type iteration for the families in a Hilbert space. Using these results, we obtain new weak and strong convergence theorems in a Hilbert space.
How to Cite this Article:
Wataru Takahashi, Weak and strong convergence theorems for families of nonlinear and nonself mappings in Hilbert spaces, J. Nonlinear Var. Anal. 1 (2017), 1-23.