TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A p -WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

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.

Download Full-text

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽

10.2298/fil1712611k ◽

2017 ◽

Vol 31 (12) ◽

pp. 3611-3626 ◽

Cited By ~ 2

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.

Download Full-text

Operators from H1 into a Banach space and vector valued measures

Geometric Aspects of Banach Spaces ◽

10.1017/cbo9780511662300.007 ◽

1989 ◽

pp. 87-93

Author(s):

Oscar Blasco

Keyword(s):

Banach Space ◽

Vector Valued

Download Full-text

Some results on the span of families of Banach valued independent, random variables

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171291000443 ◽

1991 ◽

Vol 14 (2) ◽

pp. 381-384

Author(s):

Rohan Hemasinha

Keyword(s):

Banach Space ◽

Probability Space ◽

Linear Span ◽

Random Variables ◽

Isomorphic Copy ◽

Independent Random Variables ◽

Closed Linear Span

LetEbe a Banach space, and let(Ω,ℱ,P)be a probability space. IfL1(Ω)contains an isomorphic copy ofL1[0,1]then inLEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent,Evalued mean zero random variables has infinite codimension. IfEis reflexive orB-convex and1<P<∞then the closed(in LEP(Ω))linear span of any family of independent,Evalued, mean zero random variables is super-reflexive.

Download Full-text