in [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.

If the limit of this as t → 0 exists, then we say that h(x) is Abel summable with the limit as the sum. If h(x) is integrable on R, then h is Abel summable with the usual integral of h being the Abel sum. One can show that the function At(x) can be expressed as an average of Gaussians. This is a quite useful fact, and basically it is a way of saying that Gaussians are more concentrated. For ins...

Let F be a distribution and let f be a locally summable function. The distribution F( f ) is defined as the neutrix limit of the sequence {Fn( f )}, where Fn(x) = F(x)∗δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x−sIn|x| and |x| is evaluated for s= 1,2, . . . ,μ > 0 and μs = 1,2,...

In this paper we introduce strongly $left[  V_{2},lambda_{2},M,pright]-$summable double vsequence spaces via Orlicz function and examine someproperties of the resulting these spaces. Also we give natural relationshipbetween these spaces and $S_{lambda_{2}}-$statistical convergence.

In this paper we study the convergence in distribution and local limit theorem for partial sums of linear random fields with i.i.d. innovations that have infinite second moment belong to domain attraction a stable law index $0<\alpha\leq2$ under condition are centered if $1<\alpha\leq2$ symmetric $\alpha=1$. We establish these two types theorems as long well-defined, coefficients either absolut...

The neutrix composition F (f(x))) of a distribution F (x) and a locally summable function f(x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x) = F (x) ∗ δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). It is proved that the neutrix compo...

For a function φ in L(0, 1), extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates φ(nx), n = 1, 2, 3, . . . , constitutes a Riesz basis or a complete sequence in L(0, 1). The problem translates into a question concerning multipliers and cyclic vectors in the Hilbert space H of Dirichlet series f(s) = ∑ n ann, where the coefficients an ar...

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....