In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...

Keyword: Difference equation Non-monotone argument Retarded argument Oscillatory solutions Nonoscillatory solutions Consider the first-order retarded difference equation DxðnÞ þ pðnÞx sðnÞ ð Þ 1⁄4 0; n 2 N0 where ðpðnÞÞnP0 is a sequence of nonnegative real numbers, and ðsðnÞÞnP0 is a sequence of integers such that sðnÞ 6 n 1, n P 0; and limn!1 sðnÞ 1⁄4 1. Under the assumption that the retarded ...

Let R be a commutative ring with identity. In this paper, for given monotone decreasing positive sequence and an increasing of subsets , we will define metric on using them. Then, use kind to obtain variant the proof Van der Waerden's theorem by Furstenberg [3].

Abstract The primary goal of this research is to investigate the approximate numerical solution variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In study, sequence obtained by proposed iterative technique for solving converges strongly toward a due viscosity-type scheme. Furthermore, new that uses an inertial mechanism obtain strong convergence...

We investigate when limits of graphs (graphons) and permutations (permutons) are uniquely determined by finitely many densities of their substructures, i.e., when they are finitely forcible. Every permuton can be associated with a graphon through the notion of permutation graphs. We find permutons that are finitely forcible but the associated graphons are not. We also show that all permutons th...

In speech translation, we are faced with the problem of how to couple the speech recognition process and the translation process. Starting from the Bayes decision rule for speech translation, we analyze how the interaction between the recognition process and the translation process can be modelled. In the light of this decision rule, we discuss the already existing approaches to speech translat...

In this contribution we present some interesting constructions of non-continuous triangular norms. The first approach is based on strictly increasing sequences of natural numbers. An associative commutative monotone and bounded by minimum binary operation on these sequences induces a t-norm. The corresponding t-norm is left continuous and therefore it is applicable in the fuzzy logic. Several o...

The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...

Constructions of permutation arrays are presented that are optimal or nearlyoptimal with respect to two cost measures: the so-called longest-jump measure and the longest-monotone-greedy-subsequence measure. These measures arise in the context of scheduling problems in asynchronous, shared memory, multiprocessor machines. ∗Computer Science Department, Technion — Israel Institute of Technology, H...

In this paper, we introduce a new iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common el...