Article
New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces
Authors
Abstract
In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators 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. Finally, applications of our theorems to some constrained convex minimization problems are given.
Keywords
Demicontractive mappings, Quasi-nonexpansive mappings, Common fixed points, Accretive operators, 47H05, 47H09, 47J25
Citation
Sow, T. (2019). New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in banach spaces. Applied Mathematics and Nonlinear Sciences, 4(2), 559–574. https://doi.org/10.2478/AMNS.2019.2.00053
T. Sow, “New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in banach spaces,” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, pp. 559–574, 2019, doi: 10.2478/AMNS.2019.2.00053.
Sow T. New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in banach spaces. Applied Mathematics and Nonlinear Sciences. 2019;4(2):559–574. doi:10.2478/AMNS.2019.2.00053.
Sow, T. (2019), ‘New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in banach spaces’, Applied Mathematics and Nonlinear Sciences, 4(2), pp. 559–574. Available at: https://doi.org/10.2478/AMNS.2019.2.00053.
Sow, T.m.m. “New Iterative Schemes for Solving Variational Inequality and Fixed Points Problems Involving Demicontractive and Quasi-nonexpansive Mappings in Banach Spaces.” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, 2019, pp. 559–574. https://doi.org/10.2478/AMNS.2019.2.00053.
Sow, T.m.m. “New Iterative Schemes for Solving Variational Inequality and Fixed Points Problems Involving Demicontractive and Quasi-nonexpansive Mappings in Banach Spaces.” Applied Mathematics and Nonlinear Sciences 4, no. 2 (2019): 559–574. https://doi.org/10.2478/AMNS.2019.2.00053.
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Published by: Engineering Journals
