The authors have shown [Proc. Amer. Math. Soc. 135 (2007), 4039– 4044] that every nonmetrizable, pseudocompact abelian group has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology. Here they give a comprehensive, direct and self-contained proof of this result.

Some random xed point theorems for set-valued random operators under very mild conditions are established. Some recent results of O'Regan ([Proc. Amer. Math. Soc. 126 (1998), 3045{3053] and [Computers Math. Applic. 35 (1998), 27{34]) are improved signi cantly. The discussion in this paper underlines, in addition to generality, the unifying aspects of our result.

In this paper, we obtain the Hyers–Ulam–Rassias stability of the generalized Pexider functional equation ∑ k∈K f(x+ k · y) = |K|g(x) + |K|h(y), x, y ∈ G, where G is an abelian group, K is a finite abelian subgroup of the group of automorphism of G. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ Stability Theorem that appeared in his paper: On the stability of the lin...

Caveat. This note has become seriously out of date due, among other things, to recent work by Philipp Hieronymi [Defining the set of integers in expansions of the real field by a closed discrete set. Proc. Amer. Math. Soc. 138 (2010), no. 6, 21632168. MR2596055]. In particular, the paragraph after the proof of Corollary 4 should be struck. Rather than update this particular note, we are are act...

resignation of an attorney has important effects on the principal and the process of trial. if the court or principal do not know about the resignation of the attorney, it may create irreparable losses for principal or cause prolongation of proceedings. so determining exact and comprehensive criterions about the resignation of attorney is necessary. if the attorney does not observe these criter...