In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,rese...In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.展开更多
In this paper we give some characterizations of O-convexity of Banach spaces, and show the criteria for O-convexity in Orlicz-Bochner function space LM（μ, X） and Orlicz-Bochner sequence space lM（Xs） endowed with ...In this paper we give some characterizations of O-convexity of Banach spaces, and show the criteria for O-convexity in Orlicz-Bochner function space LM（μ, X） and Orlicz-Bochner sequence space lM（Xs） endowed with Orlicz norm.Moreover, we give a sufficient condition for the dual of such a space to have the fixed point property.展开更多
Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the...Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.展开更多
In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessar...In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.展开更多
The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space....The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.展开更多
The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-norm...The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.展开更多
众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等...众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。展开更多
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
文摘In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.
文摘In this paper we give some characterizations of O-convexity of Banach spaces, and show the criteria for O-convexity in Orlicz-Bochner function space LM（μ, X） and Orlicz-Bochner sequence space lM（Xs） endowed with Orlicz norm.Moreover, we give a sufficient condition for the dual of such a space to have the fixed point property.
基金Project supported by National Natural Science Foundation of China(10371052,10671084)
文摘Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.
文摘In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.
文摘The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.
文摘The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.
文摘众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。
