An approximation theorem for linear Cauchy problems in Banach space

Banach space valued ultradistributions and applications to abstract Cauchy problems

We define the convolution of Banach space valued ultradistributions in the sense of Braun, Meise, and Taylor. We then treat abstract Cauchy problems in Banach spaces as convolution equations and give a characterization of those problems that have ultradistributional fundamental solutions. Our characterization extends in the Beurling case a result due to H.A. Emamirad. We apply our result to dif...

Asymptotic Stability of Discontinuous Cauchy Problems in Banach Space with Applications

We present an asymptotic stability result for a class of discontinuous dynamical systems (DDS) determined by differential equations in Banach space (resp., Cauchy problems on abstract spaces). We demonstrate the applicability of our result in the analysis of several important classes of DDS, including systems determined by functional differential equations and partial differential equations. Co...

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

An infinite Ramsey theorem and some Banach - space dichotomies

A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and TomczakJaegermann, this gives a positive...

BEST APPROXIMATION SETS IN -n-NORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.