The concepts of I-convergence and I-Cauchy condition are a generalization of statistical convergence and statistical Cauchy conditions and are dependent on the notion of the ideal I of subsets of the set N of positive integers. In this paper, we shall introduce two new notions of I-uniform continuity and I-uniform boundedness of a function with values in R or in a metric space and then study th...

We study triangulation schemes for the joint kernel of a diffusion process with uniformly continuous coefficients and an adapted, non-resonant Abelian process. The prototypical example of Abelian process to which our methods apply is given by stochastic integrals with uniformly continuous coefficients. The range of applicability includes also a broader class of processes of practical relevance,...

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space a...

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. In Patterson and Savas (2006) extended the definitions presented in (Patterson, 2003) to l...

We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an A2–Muckenhoupt weight. Using the so-called Xu-Zikatanov (XZ) identity, we derive a nearly uniform convergence result under the assumption that the underlying mesh is quasi-uniform. As an application we also consider the socalled α-harmonic extension to locali...

We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. show that implies and ⊤-uniform with countable bases, are equivalent. As an illustration of the applicability concept, we give a fixed point theorem certain contractive self-mappings in space. This result yields, as special case, probabilistic metric spaces.

In this work we are interested in the numerical approximation of 1D parabolic singularly perturbed problems of reaction–diffusion type. To approximate the multiscale solution of this problem we use a numerical scheme combining the classical backward Euler method and central differencing. The scheme is defined on some special meshes which are the tensor product of a uniform mesh in time and a sp...

This paper discusses the global output convergence for continuous time recurrent neural networks with continuous decreasing as well as increasing activation functions in probabilistic metric space. We establish three sufficient conditions to guarantee the global output convergence of this class of neural networks. The present result does not require symmetry in the connection weight matrix. The...