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1
Content available remote WORTH property, García-Falset coefficient and Opial property of infinite sums
Hardtke J.-D.
Commentationes Mathematicae
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2015
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Vol 55, No. 1
23--44
EN
We prove some results concerning the WORTH property and the García-Falset coefficient of absolute sums of infinitely many Banach spaces. Also, the Opial property/uniform Opial property of infinite ℓp-sums is studied, and some properties analogous to the Opial property/uniform Opial property are discussed for Lebesgue–Bochner spaces Lpμ; X.
2
Content available remote Asymptotically isometric and isometric copies of ℓ1 in some Banach function lattices
Kamińska A., Mastyło M.
Commentationes Mathematicae
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2013
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Vol. 53, No. 2
283--300
EN
We identify the class of Calderón-Lozanovskii spaces that do not contain an asymptotically isometric copy of ℓ1, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of ℓ1(n) for each integer n≥2. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of ℓ1. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of ℓ1(n) and ℓ1. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.
3
Content available remote Weak nearly uniform smoothness of the ψ-direct sums (X1 O…O XN)ψ
Kato M., Tamura T.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 2
171--198
EN
We shall characterize the weak nearly uniform smoothness of the ψ-direct sum (X1 O…O XN)ψof N Banach spaces X1,..., XN, where ψ is a convex function satisfying certain conditions on the convex set [formula]. To do this, a class of convex functions which yield l1-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular, an example which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square will be presented.
4
Content available remote Some remarks on a fixed point property for multivalued mapping
Kapeluszny J.
Journal of Mathematics and Applications
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2010
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Vol. 32
47-52
EN
In [5] T. Dominguez Benavides and B. Gavira proved that Banach spaces with [wzór] satisfy the fixed point property for nonexpansive compact convex valued multivalued mappings. We give some simplification of the proof of this theorem.
5
Content available remote Uniform non l -ness of l∞-sums of Banach spaces
Kato M., Tamura T.
Commentationes Mathematicae
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2009
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Vol. 49, [Z] 2
179-187
EN
We shall characterize the uniform non-l {...} -ness of `l∞-sums of Banach spaces (X1 ⊕ź ź ź⊕Xm)1. As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.
6
Content available Existence of solutions of some quadratic integral equations
Anichini G., Conti G.
Opuscula Mathematica
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2008
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Vol. 28, no. 4
433-440
EN
In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
7
Content available remote Uniform non-ln1-ness of l_1-sums of Banach spaces
Kato M., Tamura T.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
161-169
EN
We shall characterize the uniform non-`n1-ness of the `1-sum (X1 +ź ź ź + X_m)_1 of a finite number of Banach spaces X_1, ź ź ź ,X_m. Also we shall obtain that (X_1 +ź ź ź +X_m)_1 is uniformly non-lm+1 if and only if all X_1, . . . ,X_m are uniformly non-square (note that (X_1 + ź ź ź +X_m)_1 is not uniformly non-lm1). Several related results will be presented.
8
Content available remote Weak nearly uniform soothness and worth property of [fi]-direct sums of Banach spaces
Kato M., Tamura T.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 1
113-129
EN
We shall characterize the weak nearly uniform smoothness of the fi-direct sum X Y of Banach spaces X and Y . The Schur and WORTH properties will be also characterized. As a consequence we shall see in the [...]-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.
9
Content available remote Irreducible continua without the fixed-point property
Hagopian Ch. L.
Bulletin of the Polish Academy of Sciences. Mathematics
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2003
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Vol. 51, no 1
121-127
EN
We define a continuum of type lambda that admits a fixed-point-free map and has the condition that each of its layers has the fixed-point property. This answers a question of G. R. Gordh.
10
Content available remote General solutions of two functional inequalities and converses to contraction theorems
Jachymski J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2003
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Vol. 51, no 2
147-156
EN
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.
11
Content available remote Property (L) in Orlicz sequence spaces equipped with the Luxemburg norm
ChunXue W., Cui Y.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(2)
301-309
EN
In this paper, we prove that a banach space X with the property (L) with respect to the function [ro](r,s) has the uniform Opial property if and only if [ro](1,s)>1 for any s>0. The criterion in order that an Orlicz sequence space equipped with the Luxemburg norm has the property (L) is given.
12
Content available remote Opial's modulus in Köthe sequence spaces
Cui Y., Li Y., Płuciennik R.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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1999
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[Z] 39
43-56
EN
It is found a modified formula for Opial's modulus rX of order continuous Köthe sequence space X without Schur's property. By using this result, the Opial's modulus of Lebesgue sequence spaces as well as Cesaro sequence spaces can be computed easily. Moreover it is proved in the Köthe se-quence space X with the Fatou property the condition rX(1)>0 implies the order continuity of X.
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