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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,

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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.

In this paper, we introduce and study an algorithm for approximating zeros of A. Furthermore, we study the application of this algorithm to the approximation of Hammerstein integral equations, fixed points, convex optimization, and variational inequality problems. Finally, we present numerical and illustrative examples of our results and their applications.

<p style='text-indent:20px;'>This series of two papers is devoted to the study of the principal spectral theory of nonlocal dispersal operators with almost periodic dependence and the study of the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence. In the first part of the series, we investigated the principal spectral theory of nonlocal dispersal operators from two aspects: top Lyapunov exponents and generalized principal eigenvalues. Among others, we provided various characterizations of the top Lyapunov exponents and generalized principal eigenvalues, established the relations between them, and studied the effect of time and space variations on them. In this second part of the series, we study the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence applying the principal spectral theory developed in the first part. In particular, we study the existence, uniqueness, and stability of strictly positive almost periodic solutions of Fisher KPP equations with nonlocal dispersal and almost periodic dependence. Using the properties of the asymptotic dynamics of nonlocal dispersal Fisher-KPP equations, we also establish a new property of the generalized principal eigenvalues of nonlocal dispersal operators in this paper.</p>

Let C be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space E with dual space E * . We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a common solution of a family of variational inequality problems and a common element of fixed points of a family of a general class of nonlinear nonexpansive maps. The sequence of this new method is proved to converge strongly to a common element of the families. Our theorem and its applications complement, generalize, and extend the results of Uba, Otubo, and Onyido (Fixed