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The generalized Stokes theorem for R-linear forms on Lie algebroids

100%

Balcerzak B.

Journal of Applied Analysis

2012

tom Vol. 18, nr 1

117-131

We present the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). The Stokes formula on forms is applied to prove that two homotopic homomorphisms of Lie algebroids imply the existence of a chain operator joining their pullback operators.

Stability of the equation of ring homomorphisms

100%

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

tom Vol. 12

29-35

Let R be a unitary ring and (A,║‧║) stand for a Banach algebra with a unit. In connection with some stability results of R. Badora [1] and D.G. Bourgin [2] concerning the system of two Cauchy functional equations [formula] for mappings f : R→ A, we deal with Hyers-Ulam stability problem for a single equation f(x + y) + f(xy) = f(x) + f(y) + f(x)f(y). The basic question whether or not equation (**) is equivalent to the system (*) has widely been examined by J. Dhombres [3] and the present author in [4] and [5].