In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence{xn}n∈N by the quasi-contractive conditions of{Tn}n∈N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x of{xn}n∈N is the unique common fixed point of{Tn}n∈N. Finally, we will give more generalized common fixed point theorem for mappings{Ti,j }i,j∈N. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.
This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.
In 1981, Cohen constructed an infinite family of homotopy elements ζk∈π*(S) represented by h0bk∈ Ext3,2(p-1)(pk+1+1)A(Z/p, Z/p) in the Adams spectral sequence, where p > 2 and k≥1. In this paper,we make use of the Adams spectral sequence and the May spectral sequence to prove that the composite map ζn-1β2γs+3is nontrivial in the stable homotopy groups of spheres πt(s,n)-s-8(S), where p≥7, n > 3,0≤s < p- 5 and t(s, n) = 2(p- 1)[pn+(s + 3)p2 +(s + 4)p +(s + 3)] + s.
