Abstract
In this paper, we introduce a modified viscosity implicit rules of one asymptotically nonexpansive mapping in Hilbert spaces. Some strong convergence theorems are given under certain assumptions imposed on the parameters. As an application, we apply our main results to solve finite variational inequality problems in Hilbert spaces. A numerical example is also given to support our main results.
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This work was supported by the NSF of China (No. 11401063), the University Young Core Teacher Foundation of Chongqing (020603011714), Talent Project of Chongqing Normal University (Grant No. 02030307-00024), the Natural Science Foundation of Chongqing (cstc2017jcyjAX0006) and Science and Technology Project of Chongqing Education Committee (Grant No. KJ1703041).
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Yan, Q., Cai, G. Convergence analysis of modified viscosity implicit rules of asymptotically nonexpansive mappings in Hilbert spaces. RACSAM 112, 1125–1140 (2018). https://doi.org/10.1007/s13398-017-0413-8
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DOI: https://doi.org/10.1007/s13398-017-0413-8