T.M.M. Sow, Strong convergence of a modified Mann algorithm for multivalued quasi-nonexpansive mappings and monotone mappings with an application, Vol. 2020 (2020), Article ID 3, pp. 1-14

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DOI: 10.23952/cot.2020.3

Received April 29, 2019; Accepted February 10, 2020; Published February 29, 2020

 

Abstract. In this paper, we introduce and study a new iterative method which is a combination of a projection method and a modified Mann method for finding a common element of the set of solutions of variational inequality problems for a monotone mappings and the set of fixed points of multivalued quasi-nonexpansive mappings in an infinite dimensional Hilbert space. We prove that the sequences generated by the proposed algorithm converge strongly to a common element of in the set of common solutions. Finally, we apply our results to the problem of finding a common solution of fixed points problems involving multivalued quasi-nonexpansive mappings and optimization problems.

 

How to Cite this Article:
T.M.M. Sow, Strong convergence of a modified Mann algorithm for multivalued quasi-nonexpansive mappings and monotone mappings with an application, Communications in Optimization Theory, Vol. 2020 (2020), Article ID 3, pp. 1-14 .