Convergence theorems of solutions of a generalized variational inequality

Fixed Point Theory and Applications

关键词: nonexpansive mapping;    fixed point;    relaxed cocoercive mapping;    variational inequality;   

DOI  :  

来源: DOAJ

【 摘 要 】

Abstract

The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where r ≥ 1 is an integer and each C_m is assumed to be the solution set of a generalized variational inequality. Let C be a nonempty closed and convex subset of a real Hilbert space H. Let A_m, B_m : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r. It is proved that the sequence {x_n} generated in the following algorithm:

where u ∈ C is a fixed point, {α_n}, {β_n}, {γ_n}, {δ_(1,n)}, ..., and {δ_(r,n)} are sequences in (0, 1) and , are positive sequences, converges strongly to a solution of CFP provided that the control sequences satisfies certain restrictions.

2000 AMS Subject Classification: 47H05; 47H09; 47H10.

【 授权许可】

Unknown