Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (2): 395-407.

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Viscosity Implicit Algorithms for a Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces

Gang Cai()   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
  • Received:2018-11-20 Online:2020-04-26 Published:2020-05-21
  • Supported by:
    the NSFC(11971082);the NSFC(11771063);the NSF of Chongqing(cstc2017jcyjAX0006);the Science and Technology Project of Chongqing Education Committee(KJZD-K201900504);the University Young Core Teacher Foundation of Chongqing(020603011714);the Talent Project of Chongqing Normal University(02030307-00024)

Abstract:

In this paper, we study a viscosity implicit algorithm for finding a common element of the set of solutions of a new variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Using modified extragradient method, we obtain strong convergence theorems under some suitable assumptions imposed on the parameters. The results obtained in this paper extend and improve many recent ones.

Key words: Hilbert spaces, Nonexpansive mapping, Variational inequality, Strong convergence

CLC Number: 

  • O177
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