Abstract The notion of statistical convergence was extended to $\mathfrak{I}$ I -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the statistically $\mathfrak{A}^{\mathfrak{I}}$ A -Cauchy $\mathf...

We study the family of Fourier-Laplace transformsFα,β(z)=F.p.∫0∞tβexp⁡(itα−izt)dt,Imz<0, for α>1 and β∈C, where Hadamard finite part is used to regularize integral when Reβ≤−1. prove that each Fα,β has analytic continuation whole complex plane determine its asymptotics along any line through origin. also apply our ideas show some these functions provide concrete extremal examples Wiener-Ikehara...

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

In this paper, we obtain one-sided and two-sided Tauberian conditions of Landau Hardy types for (C,1,0) (C,0,1) summability methods improper double integrals under which convergence follows from integrals. We give similar results (C,1,1) method general, in terms the concepts slowly decreasing (resp. oscillating) strong functions different senses Ces?ro real or complex-valued locally integrable ...

A basic sequence in a Banach space is called wide-(s) if it is bounded and dominates the summing basis. (Wide-(s) sequences were originally introduced by I. Singer, who termed them P ∗-sequences.) These sequences and their quantified versions, termed λ-wide-(s) sequences, are used to characterize various classes of operators between Banach spaces, such as the weakly compact, Tauberian, and supe...

Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence sp...