Abstract
Abstract The purpose of this article is to investigate the problem of finding a common element of the solution sets of two different systems of variational inequalities and the set of fixed points a strict pseudocontraction mapping defined in the setting of a real Hilbert space. Based on the well-known extragradient method, viscosity approximation method and Mann iterative method, we propose and analyze a generalized extra-gradient iterative method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and includes the iterative methods considered in the earlier and recent literature as special cases. Our result represents the modification, supplement, extension and improvement of some corresponding results in the references. Mathematics Subject Classification (2000): Primary 49J40; Secondary 65K05; 47H09.
Highlights
Let H be a real Hilbert space with inner product 〈·, ·〉 and norm ║ · ║
It is well known that the variational inequalities are equivalent to the fixed-point problems, the origin of which can be traced back to Lions and Stampacchia [1]
Related to the variational inequalities, we have the problem of finding fixed points of nonexpansive mappings or strict pseudocontractions, which is the current interest in functional analysis
Summary
Let H be a real Hilbert space with inner product 〈·, ·〉 and norm ║ · ║. Related to the variational inequalities, we have the problem of finding fixed points of nonexpansive mappings or strict pseudocontractions, which is the current interest in functional analysis.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
