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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.

65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H30Particular nonlinear operators
47H09Mappings defined by “shrinking” properties
Full Text: DOI
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