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


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


	Fixed Point Theory, Volume 19, No. 1, 2018, 407-420, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.32 Authors: Wataru Takahashi, Ching-Feng Wen and Jen-Chih Yao Abstract: 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. Key Words and Phrases: Fixed point, demimetric mapping, inverse strongly monotone mapping, shrinking projection method, variational inequality problem. 2010 Mathematics Subject Classification: 47H05, 47H10. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents