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Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type. (English) Zbl 1215.65105
Authors’ abstract: We study a hybrid iterative scheme for finding a common element of a set of solutions of generalized mixed equilibrium problem, a set of common fixed points of a finite family of weak relatively nonexpansive mappings and null spaces of a finite family of $\gamma$-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.
##### MSC:
 65J15 Equations with nonlinear operators (numerical methods) 47J25 Iterative procedures (nonlinear operator equations) 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47H30 Particular nonlinear operators 47H09 Mappings defined by “shrinking” properties