In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n, H n (A, X) = 0 if and only if the n-th cohomology group approximately vanishes.

A polytope in R is said to be stable on a facet if and only if the perpendicular to that facet through the center of gravity meets the facet itself. One may consider the stability of a body with respect to an arbitrary "center of gravity on the interior of the body [1,3,6], or one may take the center of gravity to be determined by the shape of the body itself. Most typically, the center of grav...

We consider the action of the 2-dimensional projective general linear group PGL(2, q) on the projective line PG(1, q). A subset S of PGL(2, q) is said to be an intersecting family if for every g1, g2 ∈ S, there exists α ∈ PG(1, q) such that αg1 = αg2 . It was proved by Meagher and Spiga that the intersecting families of maximum size in PGL(2, q) are precisely the cosets of point stabilizers. We...

Control laws' design strategies are developed to stabilize a class of BIBO integro-differential systems with two distributed delays by using an extended system.

Small and Medium sized Enterprises (SMEs) make a major contribution to most western economies. They are often supported by government policies and in UK the government encourages banks to lend to them. It is generally believed that the credit crunch will have had an impact on performance of SMEs. This study looks at the impact of the crunch using large samples from 2007 through to 2010. It look...

The law of multiplicative error is presented for independent observations and correlated observations represented by the q-product, respectively. We obtain the standard log-normal distribution in the former case and the log-q-normal distribution in the latter case. Queirós’ q-log normal distribution is also reconsidered in the framework of the law of error. These results are presented with math...

We introduce the exact core and the biexact core of a strategic game form. Those are solutions which lie between the usual b-core and the set of strong equilibrium outcomes. We define the corresponding notion of exact and biexact stability. We prove that a game form is exactly stable if and only if it is exact, tight and subadditive and that it is biexactly stable if and only if in addition it ...