The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space

By Wataru Takahashi, Ching-Feng Wen, Jen-Chih Yao. 2018

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In this paper, using a new nonlinear mapping called demimetric and the shrinking projection method, we prove a strong convergence theorem for finding a common element of the set of common fixed points for a finite family of these new demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in a Hilbert space. Using the result, we obtain well-known and new strong convergence theorems in a Hilbert space.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6e763b96a7309831d5cf932de13925a1c1cf86ff