Kottman’s constant, packing constant and Riesz angle in some classes of K ¨othe sequence spaces

We have found a sufficient condition in order that the Kottman constant to be equal to the Riesz angle for Kothe ¨ sequence spaces. We have found the ball packing constant in weighted Orlicz sequence spaces, endowed with Luxemburg or p–Amemiya norm. We have calculated the Riesz angle for Musielak–Orlicz, Nakano, weighted Orlicz, Orlicz, Orlicz–Lorentz, Lorentz and Cesaro sequence spaces.

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Complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2011.01.039 ◽

2011 ◽

Vol 378 (1) ◽

pp. 151-158 ◽

Cited By ~ 4

Author(s):

Lili Chen ◽

Yunan Cui

Keyword(s):

Sequence Spaces ◽

Orlicz Sequence Spaces ◽

Amemiya Norm

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Local monotonicity coefficients in Orlicz sequence spaces equipped with the p-Amemiya norm

Journal of Inequalities and Applications ◽

10.1186/s13660-020-2291-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Xin He ◽

Yunan Cui ◽

Henryk Hudzik

Keyword(s):

Measure Space ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Orlicz Sequence Space ◽

Atomic Measure ◽

Uniform Monotonicity ◽

Orlicz Sequence Spaces ◽

Necessary And Sufficient ◽

Local Monotonicity ◽

Amemiya Norm

Abstract In this paper, the monotonicity is investigated with respect to Orlicz sequence space $l_{\varPhi , p}$ l Φ , p equipped with the p-Amemiya norm, and the necessary and sufficient condition is obtained to guarantee the uniform monotonicity, locally uniform monotonicity, and strict monotonicity for $l_{\varPhi , p}$ l Φ , p . This completes the results of the paper (Cui et al. in J. Math. Anal. Appl. 432:1095–1105, 2015) which were obtained for the non-atomic measure space. Local upper and lower coefficients of monotonicity at any point of the unit sphere are calculated, $l_{\varPhi , p}$ l Φ , p is calculated.

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M-Constants, Dominguez-Benavides coefficient, and weak fixed point property in Orlicz sequence spaces equipped with the p-Amemiya norm

Fixed Point Theory and Applications ◽

10.1186/s13663-016-0576-6 ◽

2016 ◽

Vol 2016 (1) ◽

Cited By ~ 1

Author(s):

Yunan Cui ◽

Henryk Hudzik ◽

Marek Wisła

Keyword(s):

Fixed Point ◽

Fixed Point Property ◽

Sequence Spaces ◽

Point Property ◽

Weak Fixed Point Property ◽

Orlicz Sequence Spaces ◽

Amemiya Norm

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The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces

Journal of Function Spaces ◽

10.1155/2019/8674091 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8

Author(s):

Shaoyong Zhang ◽

Meiling Zhang ◽

Yujia Zhan

Keyword(s):

Fixed Point ◽

Sequence Spaces ◽

Point Property ◽

Luxemburg Norm ◽

Continuous Norm ◽

Absolutely Continuous ◽

Uniform Smoothness ◽

Orlicz Sequence Spaces ◽

Köthe Sequence Spaces ◽

Equivalent Conditions

It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given. As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm. Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.

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Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700039137 ◽

2007 ◽

Vol 75 (2) ◽

pp. 193-210 ◽

Cited By ~ 3

Author(s):

B. Zlatanov

Keyword(s):

Sequence Space ◽

Unit Vector ◽

Sequence Spaces ◽

Unit Vector Basis ◽

Sufficient Condition ◽

Orlicz Sequence Space ◽

Property A ◽

Schur Property ◽

Vector Basis ◽

Orlicz Sequence Spaces

The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l∞, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.

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The fixed point property of Orlicz sequence spaces equipped with thep-Amemiya norm

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2013-340 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 2

Author(s):

Xin He ◽

Yunan Cui ◽

Henryk Hudzik

Keyword(s):

Fixed Point ◽

Fixed Point Property ◽

Sequence Spaces ◽

Point Property ◽

Orlicz Sequence Spaces ◽

Amemiya Norm

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Packing Constant in Orlicz Sequence Spaces Equipped with the p-Amemiya Norm

Abstract and Applied Analysis ◽

10.1155/2014/626491 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xin He ◽

Jijie Yu ◽

Yunan Cui ◽

Xin Huo

Keyword(s):

Sequence Space ◽

Geometric Characteristic ◽

Orlicz Spaces ◽

Sequence Spaces ◽

Orlicz Sequence Space ◽

Orlicz Sequence Spaces ◽

Relevant Work ◽

Amemiya Norm

The problem of packing spheres in Orlicz sequence spacelΦ,pequipped with the p-Amemiya norm is studied, and a geometric characteristic about the reflexivity oflΦ,pis obtained, which contains the relevant work aboutlp (p>1)and classical Orlicz spaceslΦdiscussed by Rankin, Burlak, and Cleaver. Moreover the packing constant as well as Kottman constant in this kind of spaces is calculated.

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