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.

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.

No abstract

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

This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.