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Received October 9, 2018; Accepted May 4, 2019; Published June 1, 2019
Abstract. In this paper, by using a modified Krasnoselskii-Mann algorithm, we introduce and study a new iterative method with a strongly accretive and Lipschitzian operator for solving a variational inequality problem with a quasi-nonexpansive maping 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. Applications are also considered in Hilbert spaces.
How to Cite this Article:
T.M.M. Sow, A new general iterative algorithm for solving a variational inequality problem with a quasi-nonexpansive mapping in Banach spaces, Communications in Optimization Theory, Vol. 2019 (2019), Article ID 9, pp. 1-12.