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General solutions of two functional inequalities and converses to contraction theorems

100%

Jachymski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

tom Vol. 51, no 2

147-156

We give necessary and sufficient conditions for the existence of some general solutions of the following two functional inequalities with an unknown real function phi: phi(Fx) is less than or equal to eta(phi(x)) and gamma(phi(Fx)) is less than or equal to phi(x). As an application we establish reciprocals to fixed point theorems of Matkowski and Wong. This extends an earlier result of Bessaga on a converse to the Banach contraction principle.

On common fixed points of commuting triangular maps

84%

Grinc M.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

tom Vol. 47, no 1

61-67

We give some conditions under which commuting triangular maps have a common fixed point. Some of them provide analogons of known results for maps of a real interval.

On linear chaos in function spaces

84%

Jimenez J. M. , Markin M. V.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

119--135

We show that, in Lp(0,∞) ( 1≤p<∞ ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞) and describe the spectra of the weighted translations provided the underlying spaces are complex.