Monotonicity Properties of Banach Lattices and Their Applications – a Survey

Journal of Mathematical Analysis and Applications

Wisła

2015

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In this paper strict monotonicity, lower and upper uniform monotonicities, uniform monotonicity as well as decreasing and increasing uniform monotonicities of Orlicz spaces equipped with the p-Amemiya norm are studied. Criteria for these six properties in the Orlicz spaces L Φ,p are given in the most general case of Orlicz function Φ and for all 1 ≤ p ≤ ∞. Finally, some applications of the results to the best dominated approximation problems are presented. This paper is a continuation of the studies from [5], [6] and [7].

Section: Applications To the Dominated Best Approximation Problemsmentioning

confidence: 99%

Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the p-Amemiya norm

Journal of Mathematical Analysis and Applications

Wisła

2015

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“…For lattice theory and monotonicity results in some Banach lattices we refer to [5][6][7][8][9][10][11][12][13][14]. Monotonicity has been extensively studied by several researchers in some specific lattices such as Lorentz, Orlicz or Musielak-Orlicz spaces [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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

2020

J Inequal Appl

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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.

“…Monotonicity properties of Banach lattices have applications in the dominated best approximation (see [6,8,14,17,24,32]) and in the fixed point theory (see [14,17,20]). They are also strongly related to the complex rotundity properties (see [29]).…”

Section: Introductionmentioning

confidence: 99%

“…Relationships between monotonicity properties and rofundity properties as well as between monotonicity properties and orthogonal monotonicity properties in Kőthe spaces were given in [22]. In abstract Banach lattices relationships between monotonicity properties and dominated best approximation problems were studied in [6,14,17].…”

Section: Introductionmentioning

confidence: 99%

Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $$\mathbb {R}^{2}$$ R 2

2019

RACSAM

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