scholarly journals A Banach space not containing $c\sb 0,\ l\sb 1$ or a reflexive subspace

1994 ◽  
Vol 344 (1) ◽  
pp. 407-420
Author(s):  
W. T. Gowers
Keyword(s):  
Banach Space ◽  
Reflexive Subspace

scholarly journals Best approximation in Orlicz spaces

1991 ◽  
Vol 14 (2) ◽  
pp. 245-252 ◽  
Author(s):  
H. Al-Minawi ◽  
S. Ayesh
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Best Approximation ◽  
Measure Space ◽  
Real Banach Space ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Finite Measure ◽  
Reflexive Subspace ◽  
Finite Measure Space

LetXbe a real Banach space and(Ω,μ)be a finite measure space andϕbe a strictly icreasing convex continuous function on[0,∞)withϕ(0)=0. The spaceLϕ(μ,X)is the set of all measurable functionsfwith values inXsuch that∫Ωϕ(‖c−1f(t)‖)dμ(t)<∞for somec>0. One of the main results of this paper is: “For a closed subspaceYofX,Lϕ(μ,Y)is proximinal inLϕ(μ,X)if and only ifL1(μ,Y)is proximinal inL1(μ,X)′​′. As a result ifYis reflexive subspace ofX, thenLϕ(ϕ,Y)is proximinal inLϕ(μ,X). Other results on proximinality of subspaces ofLϕ(μ,X)are proved.

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3611-3626 ◽  
Author(s):  
Abdul Khan ◽  
Vivek Kumar ◽  
Satish Narwal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operator ◽  
Almost Sure Stability ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Contractive Type ◽  
Bochner Integrability ◽  
Weakly Contractive

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

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