A set of positive integers is primitive (or 1-primitive) if no member divides another. Erd\H{o}s proved in 1935 that the weighted sum $\sum1/(n \log n)$ for $n$ ranging over a $A$ universally bounded all choices $A$. In 1988 he asked this universal bound attained by prime numbers. One source difficulty conjecture $\sum n^{-\lambda}$ maximized primes and only $\lambda$ at least critical exponent...

* Correspondence: [email protected] Department of Mathematics Education, Kyungnam University, Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and unifo...

For an isometric action of a finitely generated group on the ultralimit of a sequence of global Busemann nonpositive curvature spaces, we state a sufficient condition for the existence of a fixed point of the action in terms of the energy of equivariant maps from the group into the space. Furthermore, we show that this energy condition holds for every isometric action of a finitely generated gr...