Related papers: Remarks on cotype absolutely summing multilinear o…
In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.
We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
In this note, we give a simple method for computing the column sums of the Sonnenschein summability matrices.
In this paper, we study the alternating Euler $T$-sums and related sums by using the method of contour integration. We establish the explicit formulas for all linear and quadratic Euler $T$-sums and related sums. Some interesting new…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming from non-linear evolution equations.
We define a new cohomology for associative algebras which we compute for algebras with units.
Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further properties and extensions of these. Firstly, we address a…
We apply the geometric approach provided by $\Sigma$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is…
We provide an explicit formula for the coefficient polynomials of a Hermite diagonal differential operator. The analysis of the zeros of these coefficient polynomials yields the characterization of generalized Hermite multiplier sequences…
In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…
In this short note we give counterexamples to several results related to extension theorems published recently.
In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the…
This work is a collection of old and new aplications of Galois cohomology to the clasification of algebraic and arithmetical objects.
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.