223 research outputs found
Fixed point theorems for asymptotically contractive mappings
In this short paper, we prove fixed point theorems for nonexpansive mappings
whose domains are unbounded subsets of Banach spaces. These theorems are
generalizations of Penot's result in [Proc. Amer. Math. Soc., 131 (2003),
2371--2377].Comment: 7 page
An example for a one-parameter nonexpansive semigroup
We give one example for a one-parameter nonexpansive semigroup.Comment: 9 page
An easily verifiable proof of the Brouwer fixed point theorem
We give a remarkably elementary proof of the Brouwer fixed point theorem. The
proof is verifiable for most of the mathematicians.Comment: 4 page
Polymer confinement in undulated membrane boxes and tubes
We consider quantum particle or Gaussian polymer confinement between two
surfaces and in cylinders with sinusoidal undulations. In terms of the
variational method, we show that the quantum mechanical wave equations have
lower ground state energy in these geometries under long wavelength
undulations, where bulges are formed and waves are localized in the bulges. It
turns out correspondingly that Gaussian polymer chains in undulated boxes or
tubes acquire higher entropy than in exactly flat or straight ones. These
phenomena are explained by the uncertainty principle for quantum particles, and
by a "polymer confinement rule" for Gaussian polymers. If membrane boxes or
tubes are flexible, polymer-induced undulation instability is suggested. We
find that the wavelength of undulations at the threshold of instability for a
membrane box is almost twice the distance between two walls of the box.
Surprisingly we find that the instability for tubes begins with a shorter
wavelength compared to the "Rayleigh" area-minimizing instability.Comment: 6 pages, 2 figures, submitted to Phys. Rev.
Some Comments on Edelstein’s Fixed Point Theorems in ν-Generalized Metric Spaces
We study deeply two fixed point theorems in n-generalized metric spaces. The two theorems are generalizations of the famous, Edelstein’s fixed point theorem in compact metric spaces
Mizoguchi-Takahashi\u27s fixed point theorem is a real generalization of Nadler\u27s
We give an example which says that Mizoguchi-Takahashi’s fixed pointtheorem for set-valued mappings is a real generalization of Nadler’s. The example isa counterexample to a recent result in Eldred, Anuradha and Veeramani [J. Math.Anal. Appl. (2007), doi:10.1016/j.jmaa.2007.01.087]. We also give a very simple proofof Mizoguchi-Takahashi’s theorem
Numbers on Diameter in n-generalized Metric Spaces
We study some numbers on diameter in n-generalized metric spaces
On the relation between the weak Palais-Smale condition and coercivity given by Zhong
In this paper, we discuss Zhong’s result of that the weak Palais-Smalecondition implies coercivity under some assumption in [Nonlinear Anal., 29 (1997),1421–1431]. We also give a simple proof of Zhong’s result. Further we generalize theresult in Caklovic, Li and Willem [Differential Integral Equations, 3 (1990), 799–800]
Fixed point theorems and convergence theorems for some generalized nonexpansive mappings
We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition
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