in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. T...

Two types of pointwise a posteriori error estimates are presented for gradients of finite element approximations of second-order quasilinear elliptic Dirichlet boundary value problems over convex polyhedral domains Ω in space dimension n ≥ 2. We first give a residual estimator which is equivalent to ‖∇(u − uh)‖L∞(Ω) up to higher-order terms. The second type of residual estimator is designed to ...

We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains O ⊂ R with both theoretical and numerical purpose. We use N.V. Krylov’s framework of stochastic parabolic weighted Sobolev spaces H p,θ(O, T ). The summability parameters p and q in space and time may differ. Existence and uniqueness of solutions in these sp...

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes timechanged by an inverse stable subordinator whose index equals the order of the fractional time derivative. Some applications are given, to demonstrate how to specify a well-posed Dirichlet problem for space-time fractional diffusions...