In this article, we investigate the summability of formal power series solutions in time inhomogeneous heat equation with a power-law nonlinearity degree two, and variable coefficients. particular, give necessary sufficient conditions for 1-summability given direction. These generalize ones linear by W. Balser M. Loday-Richaud 2009 article [5].

In this paper we establish a Tauberian condition under which convergence follows from H"{o}lder summability of sequences of fuzzy  numbers.

We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D. A. Lutz, M. Miyake, R. Schäfke in a 1999 article ...

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Bro...

Given the Sturm-Liouville eigenfunction expansion of an ¿2 function fix), summability theory provides means for recovering the value of fix¿) at points x0 where / is sufficiently regular. If the coefficients in the expansion are perturbed slightly (in the I^ norm), a stable summation method will recover from the perturbed expansion a good approximation to fix¿). In this paper we develop stable ...

in this study we introduce the concepts of statistical convergence of order$beta$ and strong $p-$ces`{a}ro summability of order $beta$ for sequencesof fuzzy numbers. also, we give some relations between the statisticalconvergence of order $beta$ and strong $p-$ces`{a}ro summability of order$beta$ and construct some interesting examples.