Abstract
In this paper, we introduce an iterative process for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for a Lipschitz-continuous, monotone mapping in a Banach space. We obtain a strong convergence theorem for three sequences generated by this process. Our results improve and extend the corresponding results announced by many others. A simple numerical example is given to support our theoretical results.
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Acknowledgement
This work was supported by the National Natural Science Foundation of China(11401157) and the Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province in College of Mathematics and Information Science of Hebei University.
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Liu, Y., Kong, H. Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces. Indian J Pure Appl Math 50, 1049–1065 (2019). https://doi.org/10.1007/s13226-019-0373-0
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DOI: https://doi.org/10.1007/s13226-019-0373-0