Bas¸ar and Braha[1],introduced the sequence spaces˘ℓ_(∞),c˘and c˘0 of EulerCesaro bounded,convergent and null difference sequences and studied their some´properties.Then,in[2],we introduced the sequence spa...Bas¸ar and Braha[1],introduced the sequence spaces˘ℓ_(∞),c˘and c˘0 of EulerCesaro bounded,convergent and null difference sequences and studied their some´properties.Then,in[2],we introduced the sequence spaces[ℓ_(∞)]_(e.r),[c]_(e.r)and[c_(0)]_(e.r)of Euler-Riesz bounded,convergent and null difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator∆.The main purpose of this study is to introduce the sequence space[ℓ_(p)]_(e.r)of Euler-Riesz p−absolutely convergent series,where 1≤p<∞,difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator∆.Furthermore,the inclusionℓ_(p)⊂[ℓ_(p)]_(e.r)hold,the basis of the sequence space[ℓ_(p)]_(e.r)is constucted andα−,β−andγ−duals of the space are determined.Finally,the classes of matrix transformations from the[ℓ_(p)]_(e.r)Euler-Riesz difference sequence space to the spacesℓ_(∞),c and c0 are characterized.We devote the final section of the paper to examine some geometric properties of the space[ℓ_(p)]_(e.r).展开更多
In this paper, we establish some new discrete inequalities of Opial-type with two sequences by making use of some classical inequalities. These results contain as special cases improvements of results given in the lit...In this paper, we establish some new discrete inequalities of Opial-type with two sequences by making use of some classical inequalities. These results contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case.展开更多
文摘Bas¸ar and Braha[1],introduced the sequence spaces˘ℓ_(∞),c˘and c˘0 of EulerCesaro bounded,convergent and null difference sequences and studied their some´properties.Then,in[2],we introduced the sequence spaces[ℓ_(∞)]_(e.r),[c]_(e.r)and[c_(0)]_(e.r)of Euler-Riesz bounded,convergent and null difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator∆.The main purpose of this study is to introduce the sequence space[ℓ_(p)]_(e.r)of Euler-Riesz p−absolutely convergent series,where 1≤p<∞,difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator∆.Furthermore,the inclusionℓ_(p)⊂[ℓ_(p)]_(e.r)hold,the basis of the sequence space[ℓ_(p)]_(e.r)is constucted andα−,β−andγ−duals of the space are determined.Finally,the classes of matrix transformations from the[ℓ_(p)]_(e.r)Euler-Riesz difference sequence space to the spacesℓ_(∞),c and c0 are characterized.We devote the final section of the paper to examine some geometric properties of the space[ℓ_(p)]_(e.r).
基金supported by NNSF of China(11571090)GCCHB(GCC2014052)
文摘In this paper, we establish some new discrete inequalities of Opial-type with two sequences by making use of some classical inequalities. These results contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case.
