# Relations between Sequences and Selection Properties

## Related Articles

- Exact Evaluation of Infinite Series Using Double Laplace Transform Technique. Eltayeb, Hassan; Kılıçman, Adem; Mesloub, Said // Abstract & Applied Analysis;2014, p1
Double Laplace transform method was applied to evaluate the exact value of double infinite series. Further we generalize the current existing methods and provide some examples to illustrate and verify that the present method is a more general technique.

- Towards the Keldysh Tauberian Theorem. Grishin, A. F.; Poedintseva, I. V. // Journal of Mathematical Sciences;Apr2006, Vol. 134 Issue 4, p2272
New versions of the Tauberian theorem of Keldysh are proved. We give examples to show the sharpness of the conditions of these theorems. Among auxiliary results, new cases of inversion of the de l'Hospital rule are obtained. Bibliography: 14 titles.

- Asymptotically Almost Periodic Solutions of Inhomogeneous Cauchy Problems on The Half-Line. Arendt, Wolfgang; Batty, Charles J. K. // Bulletin of the London Mathematical Society;1999, Vol. 31 Issue 3, p291
Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: uâ€²(t)+Au(t)+Ï†(t)(tâ‰¥0). Suppose that u has uniformly convergent means, Ïƒ(A)âˆ©iR is countable, and Ï† is asymptotically almost periodic. Then u is asymptotically almost...

- Necessary and sufficient Tauberian conditions for certain weighted mean methods of summability. II. Móricz, F.; Rhoades, B.E. // Acta Mathematica Hungarica;2004, Vol. 102 Issue 4, p279
We prove [1, Theorems 1 and 2] under weaker conditions and in a simpler way than we did in the cited paper.

- A note on Tauberian Theorems of Exponential Type. Cadena, Meitner // International Journal of Mathematics & Computer Science;2015, Vol. 10 Issue 2, p105
Tauberian Theorems of exponential type provided by Kohlbecker, de Bruijn, and Kasahara are proved in only one Tauberian theorem. To this aim, the structure of those classical tauberian theorems is identified and, using a relationship recently proved by Cadena and Kratz, the relationships among...

- Roth's theorem with moving targets. Vojta, Paul // IMRN: International Mathematics Research Notices;1996, Vol. 1996 Issue 3, p109
The article describes the Roth's theorem with moving targets. The author proves the theorem by replacing the use of Wronskians with Schmidt's subspace theorem. He also shows that every infinite sequence as in the theorem has an infinite subsequence satisfying from this it follows that the...

- Summation Characterization of the Recessive Solution for Half-Linear Difference Equations. Došlý, Ondřej; Fišnarová, Simona // Advances in Difference Equations;2009, Special section p1
We show that the recessive solution of the second-order half-linear difference equation Î”(rkÎ¦(Î”xk)) + ck Î¦ (xk+1) = 0, Î¦(x) := |x|p-2 x,p > 1, where r, c are real-valued sequences, is closely related to the divergence of the infinite series âˆ‘âˆž (rkxkxk+1|Î”xk|p-2)-1.

- ON A GENERAL CLASS OF RENEWAL RISK PROCESS: ANALYSIS OF THE GERBER-SHIU FUNCTION. Shuanming Li; Garrido, José // Advances in Applied Probability;Sep2005, Vol. 37 Issue 3, p836
We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a Kn distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n Îµ N). The Laplace transform of the expected discounted penalty function at...

- An application of the cascade integration method. Utkina, E. // Differential Equations;Apr2007, Vol. 43 Issue 4, p586
The article discusses the case wherein the cascade integration method was applied. The cascade integration method otherwise known as the Laplace method may have several quantities with zero value in which case the value of another quantity can be expressed by quadratures. According to the...