in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

J. Ruiz-Fuertes, ∗ B. Winkler, T. Bernert, L. Bayarjargal, W. Morgenroth, M. Koch-Müller, K. Refson, V. Milman, and N. Tamura Geowissenschaften, Goethe-Universität, Altenhöferallee 1, 60438 Frankfurt am Main, Germany Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim a. d. Ruhr, Germany GFZ Potsdam, Sektion 3.3, Telegrafenberg, 14473 Potsdam, Germany Dept. of Physi...

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

Amdt, U. W., Champness, J. N., Phizackerley, R. P. & Wonawtt, A. J. (1973)J. Appl. Crystallogr. 6,457-463 Banner, D. W., Bloomer, A. C., Petsko, G. A., Phillips, D. C., Pogson, C. I., Wilson, I. A,. Corran, P. H., Furth, A. J., Milman, J. D., Offord, R. E., Priddle, J. D. & Whaley, S. G. (1975) Nature (London) 255,609-614 Harkins, R. N. & Fothergill, L. A. (1977) Biochem. SOC. Trans. 5,772-774 ...

The volume radius of a given n-dimensional body is the radius of a euclidean ball having the same volume as this body. We prove that the volume radius of a given convex symmetric n-dimensional body with diameter at most √ n is almost equal to the volume radius of a body obtained by the intersection of this body with n other bodies whose polars are bounded by 1 mean width. In the last decade, in...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.