We establish the unique solvability of a radiative-conductive heat transfer problem in system grey bodies with semitransparent inclusions and prove comparison theorem. show that higher summability data improves properties (exponential boundedness) solution.

The aim of this paper is to continue the study asymptotic expansions and summability in a monomial any number variables. In particular we characterize these terms bounded derivatives develop tauberian theorems for processes involved. Furthermore, apply Borel-Laplace analysis framework prove solutions specific class singularly perturbed PDEs.

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

In the recent papers [1, 2], the author obtained necessary and sufficient conditions for a series ∑ an which is absolutely summable of order k by a weighted mean method, 1 < k ≤ s <∞, to be such that anλn is absolutely summable of order s by a triangular matrix method. In this paper, we obtain sufficient and (different) necessary conditions for a series ∑ an which is absolutely summable |A|k to...

*Correspondence: [email protected] Department of Mathematics, İstanbul Commerce University, Sütlüce/Beyoğlu, İstanbul, Turkey Abstract Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely kth power conservative. Savaş and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we...