We give two generalizations of some known constructions of relative difference sets. The first one is a generalization of a construction of RDS by Chen, Ray-Chaudhuri and Xiang using the Galois ring GR(4,m). The second one generalizes a construction of RDS by Ma and Schmidt from the setting of chain rings to a setting of more general rings.

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...

We study the relationship between the number of minus signs in a generalized sumset, A+ · · ·+A− · · · −A, and its cardinality; without loss of generality we may assume there are at least as many positive signs as negative signs. As addition is commutative and subtraction is not, we expect that for most A a combination with more minus signs has more elements than one with fewer; however, recent...

The analysis of non-Gaussian time series has been studied extensively and has many applications. Many successful models can be viewed as special cases or variations of the generalized autoregressive moving average (GARMA) models of Benjamin et al. (2003), where a link function similar to that used in generalized linear models is introduced and the conditional mean, under the link function, assu...

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...

Let f denotes the space of almost convergent sequences, and f̂ also be the domain of the generalized di erence matrix B(r, s) in the sequence space f . The present paper is devoted to studing on the sequence spaces f̂ and f̂ s. Furthermore, the βand γ-duals of the space f̂ are determined. Finally, the classes (f̂ : μ) and (μ : f̂) of in nite matrices are characterized and the characterizations of som...

*Correspondence: [email protected] 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India Full list of author information is available at the end of the article Abstract In this paper we define the λ(u)-statistical convergence that generalizes, in a certain sense, the notion of λ-statistical convergence. We find some relations with sets of sequences which are related t...

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces h p ((F, u, Δ(r)) are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.

Charles Conley once said his goal was to reveal the discrete in the continuous. The idea here of using discrete cohomology to elicit the behavior of continuous dynamical systems was central to his program. We combine this idea with our idea of “expanders” to investigate a difference equation of the form xn = F (xn−1, . . . , xn−m) when F has a special form. Recall that the equation xn = q(xn−1)...

The main purpose of this paper is to detemine the fine spectrum of the generalized difference operator Delta_{uv} over the sequence space c0. These results are more general than the fine spectrum of the generalized difference operator Delta_{uv} of Srivastava and Kumar.