Strong convergence theorem by a hybrid method for nonlinear mappings of nonexpansive and monotone type and application. (English) Zbl 1090.49011

The authors suggest an iterative scheme for finding the common element of the set of fixed-points for the nonexpansive mapping and the set of solutions for the variational inequality for inverse strongly monotone mappings in Hilbert spaces. They prove a strong convergence theorem by the hybrid method for nonexpansive mappings and inverse strongly monotone mappings. Some applications are also obtained.


49J40 Variational inequalities
47H05 Monotone operators and generalizations
47J05 Equations involving nonlinear operators (general)
47J25 Iterative procedures involving nonlinear operators