On Some Properties of Separately Increasing Functions from [0,1]ninto a Banach Space

2014 ◽  
Vol 62 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Artur Michalak
Keyword(s):  
Banach Space ◽  
Increasing Functions

scholarly journals One-sided estimates for quasimonotone increasing functions

2003 ◽  
Vol 67 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Gerd Herzog ◽  
Roland Lemmert
Keyword(s):  
Banach Space ◽  
Normal Cone ◽  
Minkowski Functional ◽  
Order Interval ◽  
Increasing Functions

Let E be a Banach space ordered by a solid and normal cone K, and normed by the Minkowski functional of an order interval [–p, p], p ∈ K∘. We derive global one-sided estimates for quasimonotone increasing functions f : [0, T) × E → E with respect to the norm, and the distance to the line generated by p, under conditions of f; in direction p.

scholarly journals Existence and uniqueness of a solution for a minimization problem with a generic increasing function

1999 ◽  
Vol 67 (1) ◽  
pp. 85-103 ◽  
Author(s):  
A. M. Rubinov ◽  
A. J. Zaslavski
Keyword(s):  
Banach Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Bounded Sequence ◽  
Ordered Banach Space ◽  
Minimization Problems ◽  
New Type ◽  
Increasing Functions ◽  
Increasing Function ◽  
Uniqueness Of A Solution

AbstractIn this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasing norm-bounded sequence has a limit. We supply a counterexample, which shows that this property is essential and give a modification of obtained results for the space C(T), which does not possess this property.

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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