Let , , and be a strongly monotone and Lipschitz mapping. A Krasnoselskii-type sequence is constructed and proved to converge strongly to the unique solution of . Furthermore, our technique of proo f is of independent interest.

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Analysis and Optimization (to appear)), we investigate a Krasnoselskii-type iterative 454 C. E. Chidume, P. Ndambomve, A. U. Bello and M. E. Okpala algorithm for solving the multiple-sets split equality fixed point problem. Weak and strong convergence theorems are proved for two countable families of multi-valued demi-contractive mappings in real Hilbert spaces. Our theorems extend and complement some recent results of Chang et al., Chidume et al., Wu et al. and a host of other recent important results.

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 K be a nonempty closed and convex subset of a complete CAT(0) space. Let : → CB ( ) , = 1, 2, . . . , , be a family of multivalued demicontractive mappings such that := ⋂ =1 ( ) ̸ = 0. A Krasnoselskii-type iterative sequence is shown to Δ-converge to a common fixed point of the family { , = 1, 2, . . . , }. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT(0) spaces. Furthermore, our method of the proof is of special interest.

Let H be a real Hilbert space. Let $F:H\rightarrow 2^{H}$ F : H → 2 H and $K:H\rightarrow 2^{H}$ K : H → 2 H be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\in u+KFu$ 0 ∈ u + K F u has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.

Let H be a real Hilbert space, K a nonempty subset of H, and T :, where A := I -T, and I is the identity operator on K. A Krasnoselskii-type algorithm is constructed and proved to be an approximate fixed point sequence for a common fixed point of a finite family of this class of maps. Furthermore, assuming existence, strong convergence to a common fixed point of the family is proved under appropriate additional assumptions. MSC: 47H04; 47H09; 47H10

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