The purpose of this article is to formulate conjectural generalizations of Hindman’s Theorem and Ellis’s Lemma for nonassociative binary systems and relate them to the amenability problem for Thompson’s group F . Partial results are obtained for both conjectures. The paper will also contain some general analysis of the conjectures. Mathematics Subject Classification (2010): 03E02, 03E50, 05D10,...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...