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Let X be a Banach space and let Y be a separable Lindenstrauss space. We describe the Banach space P (Y, X) of absolutely summing operators as a general L1-tree space. We also characterize the BOUNDED APPROXIMATION PROPERTY and its weak version for X in terms of the space of integral operators I (X, Z*) and the space of nuclear operators N (X, Z*), respectively, where Z is a Lindenstrauss space, whose dual Z* fails to have the Radon-Nikod´ym PROPERTY.

This paper aims to investigate the stability and numerical APPROXIMATION of the Sivashinsky equations. We apply the Galerkin meshfree method based on the radial basis functions (RBFs) to discretize the spatial variables and use a group presenting scheme for the time discretization. Because the RBFs do not generally vanish on the boundary, they can not directly approximate a Dirichlet boundary problem by Galerkin method. To avoid this di culty, an auxiliary parametrized technique is used to convert a Dirichlet boundary condition to a Robin one. In addition, we extend a stability theorem on the higher order elliptic equations such as the bihar-monic equation by the eigenfunction expansion. Some experimental results will be presented to show the performance of the proposed method.

We present an isometric version of the complementably universal Banach space P with a Schauder decomposition. The space P is isomorphic to Pe lczynski's space with a universal basis as well as to Kadec’ complementably universal space with the BOUNDED APPROXIMATION PROPERTY.

In this paper, a new definition of fuzzy BOUNDED sets and totally fuzzy BOUNDED sets is introduced and properties of such sets are studied. Then a relation between totally fuzzy BOUNDED sets and N-compactness is discussed. Finally, a geometric characterization for fuzzy totally BOUNDED sets in I- topological vector spaces is derived.

A characteriation of continuity of the p-L-variation function is given and the Helly’s selection principle for LBV(p) functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class LBV(p) is found.