Convergence analysis for fixed point problem of asymptotically nonexpansive mappings and variational inequality problem in Hilbert spaces

Abstract

The purpose of this paper is to study a new viscosity iterative algorithm for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping and the set of solutions of a new variational inequality problem involving inverse-strongly monotone operators in Hilbert spaces. We prove some strong convergence theorems under some suitable assumptions imposed on the parameters by using a modified extragradient method. The results obtained in this paper may be an improvement of many recent ones in this fields.

Keywords:

• Strong convergence
• variational inequality
• fixed point
• asymptotically nonexpansive mapping
• Hilbert spaces

2000 AMS Subject Classifications:

• 47H09
• 47H10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the NSF of China [grant nos. 11571194, 11731010, 11771063], the Natural Science Foundation of Chongqing [cstc2017jcyjAX0006], Science and Technology Project of Chongqing Education Committee [grant nos. KJZD-K201900504, KJQN201801205], Talent Project of Chongqing Normal University [grant no. 02030307-00024], and Fundamental Research Funds for the Central Universities (No. 3122019142).