Abstract In this paper, we prove some properties of weighted Cesàro and Copson sequences spaces by establishing factorization theorems. The results lead to two-sided norm discrete inequalities with best possible constants also give conditions for the boundedness generalized Hardy operators.

A short proof of the classic Hardy inequality is presented for p-norms with p>1. Along lines this a sharpened version proved recent generalization Hardy’s in terminology probability theory. theoretic Copson’s discussed as well. Also 0<p<1 generalizations and Copson are proved.

If z= —1, (5) reduces to Copson's series. Ramanujan's approximation for S„(l) is, in view of (5), a considerably more singular result than it would otherwise appear. References 1. E. T. Copson, An approximation connected with e~x, Proc. Edinburgh Math. Soc. (2) 3 (1932-33), 201-206. 2. S. Ramanujan, Collected papers, p. 26, Cambridge, 1927. 3. G. Szegö, Über einige von S. Ratnanujan gestellte A...

This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s and integration parts Our investigations unify extend some continuous their corresponding discrete analogues. In addition, when α = 1, we obtain ...

We address the optimal constants in strong and weak Stechkin inequalities, both their discrete continuous variants. These inequalities appear characterization of approximation spaces which arise from sparse or have applications to interpolation theory. An elementary proof a constant inequality given by Bennett is provided, we improve Levin Copson. Finally, minimal are presented.

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration parts formula, and Hölder inequality When γ=1, then we obtain some well-known time-scale due to Hardy. As special cases, continuous discrete inequalities. Symmetry plays an essential role in determining correct methods solve