The idea of I-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of (Δ(m), I)-statistical convergence of order α and strong (Δ(p)(m), I)-Cesàro summability of order α of real sequences and investigated their relationship.

Let (pn) and (qn) be any two non-negative real sequences with Rn := n ∑ k=0 pkqn−k 6= 0 (n ∈ N). And E1 n− Euler summability method. Let (xn) be a sequence of real or complex numbers and set N p,qE 1 n := 1 Rn n ∑

In this paper we introduce strong $I^K$-convergence of functions which is common generalization of strong $I^*$-convergence of functions in probabilistic metric spaces. We also define and study strong $I^{K}$-limit points of functions in same space.

We consider a perturbed system of exponents { en } n∈Z, when the sequence {λn }n∈Z has a definite asymptotics. We study basis properties (completeness, minimality, basicity) of this system in Lebesgue space of functions Lp(·) (−π, π) with variable summability exponent p(·), subject to parameters contained in the asymptotics {λn}n∈Z.

In this note the almost sure convergence of stationary, '-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fullllment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.

For the Itô stochastic equations in Rd with drift Ld, several results are discussed, such as existence of weak solutions, corresponding Markov process, Aleksandrov type estimates their Green’s functions, which yield summability to power d/(d−1), Fabes–Stroock estimates, show that functions summable a higher degree, Fanghua Lin one main tools Wp2-theory fully nonlinear elliptic equations, fact c...

In this paper we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.