ABSTRACT. In this paper we prove some new dynamic inequalities on discrete time scales. These new inequalities contain some generalizations of the discrete inequalities due to Hardy, Copson, Leindler and Walsh. The main results will be proved using a general algebraic inequality and Keller’s chain rule on time scales. AMS (MOS) Subject Classification. 26A15, 26D10, 26D15, 39A13, 34A40. 34N05.

In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing function...

We investigate the structure of optimal domains for Hardy-type operators including, example, classical Cesàro, Copson and Volterra as well some their generalizations. prove that, in sense, abstract Cesàro

The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted `p spaces and the corresponding Lorentz sequence spaces d(w, p), with the power weighting sequence wn = n−α or the variant defined by w1 + · · ·+wn = n1−α. Exact values are found in each case except for the averaging operator with wn = n−α, for which estimates deriv...

We construct examples of centrally harmonic spaces by generalizing work Copson and Ruse. show that these are generically not at other points. use this construction to exhibit manifolds which conformally flat but such their density function agrees with Euclidean space.

This work applies machine learning to holistically interrogate the influence of metallurgical factors, such as chemical composition, heat treatment, and mechanical properties, on stress corrosion cracking resistance corrosion-resistant alloys. Particularly, we explored effect nickel in reducing susceptibility boiling magnesium chloride, arguably a controversial topic since Copson’s 1959 seminal...

This paper is devoted to the nabla unification of discrete and continuous Hardy-Copson type inequalities. Some obtained inequalities are counterparts their delta versions while others new even for discrete, continuous, cases. Moreover, these dynamic not only generalize unify related ones in literature but also improve them special