No abstract

Let C be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space E with dual space E * . A novel hybrid method for finding a solution of an equilibrium problem and a common element of fixed points for a family of a general class of nonlinear nonexpansive maps is constructed. The sequence of the method is proved to converge strongly to a common element of the family and a solution of the equilibrium problem. Finally, an application of our theorem complements, generalizes and extends some recent important results (Takahashi et al., Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces,

No abstract

A Krasnoselskii-type algorithm is constructed and proved to be an approximate fixed point sequence for a countable family of multi-valued strictly pseudo-contractive mappings in a real Hilbert space. Under some additional mild conditions, the sequence is proved to converge strongly to a common fixed point of the family. Our theorems complement and improve the results of Chidume and Ezeora [6], Abbas et al. [1], Chidume et al. [5] and a host of other important results.

Let X be a uniformly convex and uniformly smooth real Banach space with dual space X * . Let F : X → X * and K : X * → X be bounded maximal monotone mappings. Suppose the Hammerstein equation u + KF u = 0 has a solution. An iteration sequence is constructed and proved to converge strongly to a solution of this equation.