scholarly journals Convergence theorem of Pettis integrable multivalued pramart

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
M'Hamed El-Louh ◽  
Mohammed El Allali ◽  
Fatima Ezzaki
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Almost Sure Convergence ◽  
Stopping Times ◽  
Weakly Compact ◽  
Content Type ◽  
Convergence Results ◽  
The Family ◽  
Vector Valued ◽  
Generally True

PurposeIn this work, the authors are interested in the notion of vector valued and set valued Pettis integrable pramarts. The notion of pramart is more general than that of martingale. Every martingale is a pramart, but the converse is not generally true.Design/methodology/approachIn this work, the authors present several properties and convergence theorems for Pettis integrable pramarts with convex weakly compact values in a separable Banach space.FindingsThe existence of the conditional expectation of Pettis integrable mutifunctions indexed by bounded stopping times is provided. The authors prove the almost sure convergence in Mosco and linear topologies of Pettis integrable pramarts with values in (cwk(E)) the family of convex weakly compact subsets of a separable Banach space.Originality/valueThe purpose of the present paper is to present new properties and various new convergence results for convex weakly compact valued Pettis integrable pramarts in Banach space.

scholarly journals Decompositions of Weakly Compact Valued Integrable Multifunctions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 863 ◽  
Author(s):  
Luisa Di Piazza ◽  
Kazimierz Musiał
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Compact Convex ◽  
Weakly Compact ◽  
Seminal Paper ◽  
Decomposition Property ◽  
Short Overview ◽  
Decomposition Theorems ◽  
State Of Art

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.

scholarly journals Strong laws of large numbers for arrays of rowwise independent random elements

1987 ◽  
Vol 10 (4) ◽  
pp. 805-814 ◽  
Author(s):  
Robert Lee Taylor ◽  
Tien-Chung Hu
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Complete Convergence ◽  
Almost Sure Convergence ◽  
Random Variable ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Rowwise Independent ◽  
Uniformly Bounded

Let{Xnk}be an array of rowwise independent random elements in a separable Banach space of typep+δwithEXnk=0for allk,n. The complete convergence (and hence almost sure convergence) ofn−1/p∑k=1nXnk to 0,1≤p<2, is obtained when{Xnk}are uniformly bounded by a random variableXwithE|X|2p<∞. When the array{Xnk}consists of i.i.d, random elements, then it is shown thatn−1/p∑k=1nXnkconverges completely to0if and only ifE‖X11‖2p<∞.

scholarly journals The Dunford-Pettis property on vector-valued continuous and bounded functions

1993 ◽  
Vol 48 (2) ◽  
pp. 303-311 ◽  
Author(s):  
Jose Aguayo ◽  
Jose Sanchez
Keyword(s):  
Banach Space ◽  
Regular Space ◽  
Weakly Compact ◽  
Completely Regular ◽  
Bounded Functions ◽  
Continuous Operators ◽  
Vector Valued

Let X be a completely regular space, E a Banach space, Cb(X, E) the space of all continuous, bounded and E-valued functions defined on X, M(X, L(E, F)) the space of all L(E, F)-valued measures defined on the algebra generated by zero subsets of X. Weakly compact and β0-continuous operators defined from Cb(X, E) into a Banach space F are represented by integrals with respect to L(E, F)-valued measures. The strict Dunford-Pettis and the Dunford-Pettis properties are established on (Cb(X, E), βi), where βi denotes one of the strict topologies β0, β or β1, when E is a Schur space; the same properties are established on (Cb(X, E), β0), when E is an AM-space or an AL-space.

The Andersen-Jessen theorem revisited

1987 ◽  
Vol 102 (2) ◽  
pp. 351-361
Author(s):  
Klaus D. Schmidt
Keyword(s):  
Stochastic Processes ◽  
Almost Sure Convergence ◽  
Signed Measure ◽  
Convergence Theorems ◽  
Conditional Expectations ◽  
The Family ◽  
Set Function ◽  
Vector Valued

AbstractFor stochastic processes which are induced by a signed measure, the Andersen-Jessen theorem asserts almost sure convergence and yields the identification of the limit. This result has been extended to real and vector-valued stochastic processes which are induced by a finitely additive set function or a set function process. In the present paper, we study the structure of such induced stochastic processes in order to locate the Andersen-Jessen theorem and its extensions in the family of convergence theorems for martingales and their generalizations. As an application of these results, we also show that the Andersen-Jessen theorem and its extensions can be deduced from the convergence theorems for conditional expectations and positive supermartingales.

Convergence of multivalued mils and pramarts in spaces without the RNP

2003 ◽  
Vol 40 (1-2) ◽  
pp. 13-31
Author(s):  
G. Krupa
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Compact Convex ◽  
Property A ◽  
Convergence Results ◽  
Nikodym Property ◽  
Convex Subsets

New convergence results for multivalued martingales in the limit and super- and subpramarts whose values are weakly or strongly compact convex subsets of a separable Banach space are presented. In contrast to the previous results the underlying Banach space does not have the Radon-Nikodym property. A connection between multivalued and single-valued subpramarts is established. New onvergence results for single-valued mils and super- and subpramarts follow from the multivalued results presented here.

The effects of goals attainment on CEO-owner satisfaction and the role of family involvement

2019 ◽  
Vol 10 (2) ◽  
pp. 116-127
Author(s):  
Ondřej Machek ◽  
Jiří Hnilica
Keyword(s):  
Family Involvement ◽  
Family Business ◽  
Firm Value ◽  
Family Firms ◽  
Hierarchical Regression ◽  
Content Type ◽  
Business Goals ◽  
Growth Increase ◽  
The Family ◽  
Owner Satisfaction

Purpose The purpose of this paper is to examine how the satisfaction with economic and non-economic goals achievement is related to the overall satisfaction with the business of the CEO-owner, and whether family involvement moderates this relationship. Design/methodology/approach Based on a survey among 323 CEO-owners of family and non-family businesses operating in the Czech Republic, the authors employ the OLS hierarchical regression analysis and test the moderating effects of family involvement on the relationship between the satisfaction with different goals attainment and the overall satisfaction with the business. Findings The main finding is that family and non-family CEO-owner’s satisfaction does not differ significantly when economic goals (profit maximisation, sales growth, increase in market share or firm value) and firm-oriented non-economic goals (satisfaction of employees, corporate reputation) are being achieved; both classes of goals increase the overall satisfaction with the firm and the family involvement does not strengthen this relationship. However, when it comes to external non-economic goals related to the society or environment, there is a significant and positive moderating effect of family involvement. Originality/value The study contributes to the family business literature. First, to date, most of the studies focused on family business goals have been qualitative, thus not allowing for generalisation of findings. Second, there is a lack of evidence on the ways in which family firms integrate their financial and non-financial goals. Third, the authors contribute to the literature on the determinants of personal satisfaction with the business for CEOs, which has been the focus on a relatively scarce number of studies.

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

scholarly journals Draft Genome Sequences of Three Flavobacterium psychrophilum Strains Isolated from Diseased Ayu (Plecoglossus altivelis altivelis) Caught at Three Sites in the Kagami River in Kochi, Japan

2019 ◽  
Vol 8 (34) ◽  
Author(s):  
Hazuki Yamashita ◽  
Takayuki Wada ◽  
Yusuke Kato ◽  
Takuji Ikeda ◽  
Masayuki Imajoh
Keyword(s):  
Draft Genome ◽  
Psychrophilic Bacterium ◽  
Genome Sequences ◽  
Plecoglossus Altivelis ◽  
Gram Negative ◽  
Content Type ◽  
Flavobacterium Psychrophilum ◽  
Skin Ulcers ◽  
The Family

Flavobacterium psychrophilum is a Gram-negative, psychrophilic bacterium within the family Flavobacteriaceae. Here, we report the draft genome sequences of three F. psychrophilum strains isolated from skin ulcers of diseased ayu caught by tomozuri angling at three sites in the Kagami River in Japan.

scholarly journals The Blum-Hanson Property

2019 ◽  
Vol 6 (1) ◽  
pp. 92-105
Author(s):  
Sophie Grivaux
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Separable Banach Space ◽  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Theoretic Motivation

AbstractGiven a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, y ∈ X are such that Tnx tends weakly to y in X as n tends to infinity, the means{1 \over N}\sum\limits_{k = 1}^N {{T^{{n_k}}}x} tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lefèvre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lefèvre-Matheron, we characterize the compact metric spaces K such that the space C(K) has the Blum-Hanson property.

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