Results 31 to 40 of about 59 (59)

Proximinal subspaces of A(K) of finite codimension

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2501-2505, 2003., 2003
We study an analogue of Garkavi′s result on proximinal subspaces of C(X) of finite codimension in the context of the space A(K) of affine continuous functions on a compact convex set K. We give an example to show that a simple‐minded analogue of Garkavi′s result fails for these spaces.
T. S. S. R. K. Rao
wiley   +1 more source

On k‐nearly uniform convex property in generalized Cesàro sequence spaces

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 57, Page 3599-3607, 2003., 2003
We define a generalized Cesàro sequence space ces(p), where p = (pk) is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show that ces(p) is k‐nearly uniform convex (k‐NUC) for k ≥ 2 when limn→∞infpn > 1. Moreover, we also obtain that the Cesàro sequence space cesp(where 
Winate Sanhan, Suthep Suantai
wiley   +1 more source

DP1 and completely continuous operators

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 37, Page 2375-2378, 2003., 2003
W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞, (⊕α∈𝒜Xα) p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα) ∞. In fact, we show that (⊕α∈𝒜Xα) ∞ has the DP1 property if and only if it has the Dunford‐Pettis property.
Elizabeth M. Bator, Dawn R. Slavens
wiley   +1 more source

Tight Embeddability of Proper and Stable Metric Spaces

Analysis and Geometry in Metric Spaces, 2015
We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We
Baudier F., Lancien G.
doaj   +1 more source

A renorming of ℓ2, rare but with the fixed‐point property

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 65, Page 4115-4129, 2003., 2003
We give an example of a renorming of ℓ2 with the fixed‐point property (FPP) for nonexpansive mappings, but which seems to fall out of the scope of all the commonly known sufficient conditions for FPP.
Antonio Jiménez-Melado, Enrique Llorens-Fuster   +1 more
wiley   +1 more source

On the modulus of u‐convexity of Ji Gao

Abstract and Applied Analysis, Volume 2003, Issue 1, Page 49-54, 2003., 2003
We consider the modulus of u‐convexity of a Banach space introduced by Ji Gao (1996) and we improve a sufficient condition for the fixed‐point property (FPP) given by this author. We also give a sufficient condition for normal structure in terms of the modulus of u‐convexity.
Eva María Mazcuñán-Navarro
wiley   +1 more source

Convergence theorems for generalized projections and maximal monotone operators in Banach spaces

Abstract and Applied Analysis, Volume 2003, Issue 10, Page 621-629, 2003., 2003
We study a sequence of generalized projections in a reflexive, smooth, and strictly convex Banach space. Our result shows that Mosco convergence of their ranges implies their pointwise convergence to the generalized projection onto the limit set. Moreover, using this result, we obtain strong and weak convergence of resolvents for a sequence of maximal ...
Takanori Ibaraki, Yasunori Kimura, Wataru Takahashi   +2 more
wiley   +1 more source

Nonsurjective Coarse Isometries of Uniformly Convex Banach Spaces

Journal of Function Spaces, Volume 2024, Issue 1, 2024.
We apply Pisier’s inequality to establish the stability property of nonsurjective coarse isometries from a Banach space to a uniformly convex space. Making use of this result, we extend some known conclusions on (ε, p) isometries of Hilbert spaces and Lq spaces.
Yuqi Sun, Nikhil Khanna
wiley   +1 more source

Some extremal properties of section spaces of Banach bundles and their duals

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 10, Page 563-572, 2002., 2002
When X is a compact Hausdorff space and E is a real Banach space there is a considerable literature on extremal properties of the space C(X, E) of continuous E‐valued functions on X. What happens if the Banach spaces in which the functions on X take their values vary over X?
D. A. Robbins
wiley   +1 more source

Relative Uniform Convergence of Quantum Difference Sequence of Functions Related to ℓp-Space Defined by Orlicz Function

Annales Mathematicae Silesianae
The sequence spaces ruℓ∞(𝒪, ∇q), ruℓp(𝒪, ∇q), ruc(𝒪, ∇q), ruc0(𝒪, ∇q), rumϕ(𝒪, ∇q, p), runϕ(𝒪, ∇q, p), rumϕ(𝒪, ∇q), runϕ(𝒪, ∇q) are defined by the Orlicz function in this article.
Debbarma Diksha, Tripathy Binod Chandra
doaj   +1 more source