A sequence fxng generates by the formula x_{n+1} =(1- £\\_n)x_n+ £\\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {£\\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications.

The dissemination of disinformation is unwanted, but on the rise in Sweden, often via social media. Since the deliberative democratic ideal stresses the importance of good democratic dialogues, this study therefore aims at giving an answer to the question of how this theory claims disinformation in the comment section on social media should be handled. Via a normative given-that analysis the question is analysed from a normative perspective, based on what is required for a conversation to be deliberative, and problematized from a practical perspective. The analysis shows that disinformation disturbs the conversation, and thereby normatively should be erased. Meanwhile, the problematization shows that practically deleting a comment could go against the ideal, since only comments which are intended to misinform should be deleted, and the question of whether such an intent exists can be hard to determine. To solve the feasibility problem and thereby give the research question a clear answer, a theory development of the deliberative theory is being made. The essay concludes that following the new way of seeing the deliberative ideal, the comments which are suspected to contain disinformation should be left in the comment section, but ideally thoroughly via a deliberative conversation be questioned.

In this paper we discuss iterative algorithms for solving the split feasibility problem (SFP). We study the CQ algorithm from two approaches: one is an optimization approach and the other is a fixed point approach. We prove its convergence first as the gradient-projection algorithm and secondly as a fixed point algorithm. We also study a relaxed CQ algorithm in the case where the sets C and Q are level sets of convex functions. In such case we present a convergence theorem and provide a different and much simpler proof compared with that of Yang [7].

No description available.