Band 32, Heft 3 -

We propose new constructions of the approximate solutions of discrete linear differential equations and their inverse source problems. This is mainly based on a reproducing kernel Hilbert spaces approach where different types of spaces are naturally considered as a consequence of the method. Here, the major influence will be given by the Paley–Wiener and Sobolev spaces.

The sequence space BV σ was introduced and studied by Mursaleen [10]. In this article we introduce the sequence space BV I σ and study some of the properties of this space.

In the paper, the famous Hermite–Hadamard integral inequality for convex functions is generalized to and refined as the ones for n -time differentiable functions which are s -convex in the second sense, and some known results are improved.

The main objective of this paper is to introduce the Hankel–Hausdorff operator of a function f  ∈  L 1 (0,∞) generated on the Hardy space and to study its various properties in L 1 (0,∞).

The sparse binomial-type polynomials arise naturally in connection with the expected number of independent sets of a graph of order n . In this paper we find, for a fixed 0 <  z  < 1, upper and lower bounds for the values of these polynomials, as well as asymptotics for their logarithms.

In the paper, by setting up an integral identity and using Hölder integral inequality, the authors establish some new inequalities of Hermite–Hadamard type for n -time differentiable and m -convex functions and discuss applications of these inequalities to special means.