Papers by Mariusz Szczepanik
We present here an open problem concerning lipschitzian self map- pings of closed convex subsets ... more We present here an open problem concerning lipschitzian self map- pings of closed convex subsets of Banach spaces.
Moduli R(a,X) and M(X) of direct sums of Banach spaces
Journal of Mathematical Analysis and Applications, 2018
Abstract The moduli R ( a , X ) and M ( X ) , introduced by Dominguez Benavides, play an importan... more Abstract The moduli R ( a , X ) and M ( X ) , introduced by Dominguez Benavides, play an important role in the fixed point theory for nonexpansive mappings. In the paper we show that if inf i ∈ I M ( X i ) > 1 , then M ( ( ⨁ i ∈ I X i ) Z ) > 1 , where ( ⨁ i ∈ I X i ) Z is the direct sum of Banach spaces X i with respect to a Banach lattice Z , under some conditions for Z and I . Similar results are obtained for the modulus R ( a , X ) .
Topological Methods in Nonlinear Analysis, 2019
We prove that if a Banach space X has the weak fixed point property and Y satisfies the condition... more We prove that if a Banach space X has the weak fixed point property and Y satisfies the condition M (Y) > 1, then the direct sum X ⊕ Y with a uniformly convex norm has the weak fixed point property.
Fixed Point Theory, 2017
Let H be an at least two-dimensional real Hilbert space with the unit sphere S H. For α ∈ [−1, 1]... more Let H be an at least two-dimensional real Hilbert space with the unit sphere S H. For α ∈ [−1, 1] and n ∈ S H we define an (α, n)-spherical cap by Sα,n = {x ∈ S H : x, n ≥ α}. We show that the distance between the set of contractions T : Sα,n → Sα,n and the identity mapping is positive iff α < 0. We also study the fixed point property and the minimal displacement problem in this setting for nonexpansive mappings.
On local Milman’s moduli
Journal of Convex Analysis
On Milman’s moduli for Banach spaces
ABSTRACT
We present here an open problem concerning lipschitzian self map- pings of closed convex subsets ... more We present here an open problem concerning lipschitzian self map- pings of closed convex subsets of Banach spaces.
Integration of semi-infinite Toda chain in some class of unbounded solutions
Reports on Mathematical Physics, 1997
The method of solving the Cauchy problem for semi-infinite Toda chains in some class of unbounded... more The method of solving the Cauchy problem for semi-infinite Toda chains in some class of unbounded solutions is described in terms of the spectral theory for Jacobi matrices.
Bulletin of the Australian Mathematical Society, 2000
A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the be... more A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T : Aθ,p → Bθ,p for all 0 < θ < 1 and 1 < P < ∞.
A new measure of weak noncompactness is introduced. A log-arithmic convexity-type result on the b... more A new measure of weak noncompactness is introduced. A log-arithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T: Aθ,p → Bθ,p for all 0 < θ < 1 and 1 < p <∞.
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2018
In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of i... more In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.
Journal of Mathematical Analysis and Applications, 2005
We introduce and study the class of nearly uniformly noncreasy Banach spaces. It is proved that t... more We introduce and study the class of nearly uniformly noncreasy Banach spaces. It is proved that they have the weak fixed point property. A stability result for this property is obtained.
Abstract and Applied Analysis, 2001
We show that infinite dimensional geometric moduli introduced by Milman are strongly related to n... more We show that infinite dimensional geometric moduli introduced by Milman are strongly related to nearly uniform convexity and nearly uniform smoothness. An application of those moduli to fixed point theory is given.
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Papers by Mariusz Szczepanik