Suzuki, Strong convergence of Krasnoselskii
and Man's type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J.
Our analysis relies on the Krasnoselskii
fixed point theorem combined with the technique of measure of weak noncompactness.
Using some existence results for inequalities with pseudomonotone operators and convex functionals, which naturally arise in this slip problem, and the Krasnoselskii
theorem on continuity of the Nemytskii operator , we establish sufficient conditions for the existence of weak solutions and derive their energy estimates.
Moreover, it is known (see, ) that the Picard-Krasnoselskii hybrid iterative process converges faster than all of Picard, Mann, Krasnoselskii
, and Ishikawa iterative processes.
Avramescu, "Some remarks on a fixed point theorem of Krasnoselskii
," Electronic Journal of Qualitative Theory of Differential Equations, No.
AGARWAL and O'REGAN, FPTA (2009) --The authors present new Leray-Schauder alternatives, Krasnoselskii
and Lefschetz fixed point theory for multimaps between Frechet spaces.
For example, Song and Cao  have established some sufficient conditions to ensure the existence and uniqueness of the nontrivial solution by using the contraction mapping principle, Krasnoselskii
fixed point theorem, and the inequality technique, in which uniform stability conditions of fractional-order neural networks are also derived in fixed time-intervals.
Taoudi, Schaefer- Krasnoselskii
fixed point theorems using a usual measure of weak noncompactness, J.
Torres, "Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii
fixed point theorem," Journal of Differential Equations, vol.
The Orlicz sequence spaces are the special cases of Orlicz spaces studied in Krasnoselskii
and Rutickii (1961).
Suzuki: Strong convergence of Krasnoselskii
and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J.
) Let X bea Banach space, K [subset or equal to] X be a cone, and suppose that [[OMEGA].sub.1], [[OMEGA].sub.2] are open subsets of X with 0 [member of] [[OMEGA].sub.1] and [[bar.OMEGA].sub.1] [subset] [[OMEGA].sub.2].