The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn, there exist a pair of disjoint faces in the domain whose images intersect in Rn. The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakeable, but a proof that the Topological Radon Theorem follows from Borsuk-Ulam is not immediate. In...

To study the convergence to equilibrium in random maps, we develop the spectral theory of the corresponding transfer (Perron— Frobenius) operators acting in a certain Banach space of generalized functions (distributions). The random maps under study in a sense fill the gap between expanding and hyperbolic systems, since among their (deterministic) components there are both expanding and contrac...

The stability problem of functional equations started with the question concerning stability of group homomorphisms proposed by Ulam 1 during a talk before a Mathematical Colloquium at the University of Wisconsin, Madison. In 1941, Hyers 2 gave a partial solution of Ulam’s problem for the case of approximate additive mappings in the context of Banach spaces. In 1978, Rassias 3 generalized the t...

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

Ambulatory accelerometry is a technique that allows objective measurement of aspects of everyday human behavior. The aim of our research has been to develop, validate, and apply this technique, which recently resulted in an upper limb activity monitor (ULAM). The ULAM consists of body-mounted acceleration sensors connected to a waist-worn data recorder and allows valid and objective assessment ...

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

In combinatorial problems it is sometimes possible to define a G-equivariant mapping from a space X of configurations of a system to a Euclidean space Rm for which a coincidence of the image of this mapping with an arrangement A of linear subspaces insures a desired set of linear conditions on a configuration. BorsukUlam type theorems give conditions under which no G-equivariant mapping of X to...