... xnj= Δxj and τjconsists of the elements of σ which exceed sj. Note that zj(i)is a term in the sequence with fixed j and running i.2 Journal of Inequalities and Applications In [2], the ... olak and M. Et, “On some difference sequence sets and their topological properties,” Bulletinof the Malaysian Mathematical Sciences Society , vol. 28, no. 2, pp. 125–130, 2005.[6] M. Et and R. ... 4 Journal of Inequalities and ApplicationsSince εj−1+ εj< 1, we have1φsn∈σzj(n)≤εj−1+ εj< 1, (2.6)for all j∈ N and s ≥ 1. Hencenj=1zjm(φ,p,Δ)=nj=1sj−1i=1zj(i)ei+sji=sj−1+1zj(i)ei+i∈τjzj(i)eim(φ,p,Δ)≤nj=1sj−1i=1zj(i)eim(φ,p,Δ)+nj=1sji=sj−1+1zj(i)eim(φ,p,Δ)+nj=1i∈τjzj(i)eim(φ,p,Δ)≤nj=1sji=sj−1+1zj(i)eim(φ,p,Δ)+2nj=1εj,nj=1sji=sj−1+1zj(i)eipm(φ,p,Δ)=nj=1sups≥1supτj−1∈Ꮿs1φsi∈τj−1zj(i)p≤nj=1sups≥1supσ∈Ꮿs1φsi∈σzj(i)p≤n.(2.7)Therefore...