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On the domain of implicit functions in a projective limit setting without additional norm estimates

100%

Magnot J.-P.

2020

tom Vol. 53, nr 1

112--120

We examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse function theorem is obtained, and we finish with an open question on the adequate (generalized) notion of differentiation, needed for the corresponding version of the Fröbenius theorem.

Second order evolution equations with nonlocal conditions

58%

Benchohra M. , Nieto J. J. , Rezoug N.

Demonstratio Mathematica

2017

tom Vol. 50, nr 1

309--319

In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.

Regular covers and metrization

58%

Lin S.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

tom Vol. 50, no 4

427-432

In this paper it is showed that a regular and k-space with a regular k-network is metrizable, which generalized related results of A. Archangielskiĭ, H. W. Martin, M. Sakai, K. Tamano and Y. Yajima.