On continuity properties of some classes of vector-valued functions

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
K. Naralenkov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuity Properties ◽  
Weakly Continuous ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractWe extend the V BG* property to the context of vector-valued functions and give some characterizations of this property. Necessary and sufficient conditions for vector-valued VBG* functions to be continuous or weakly continuous, except at most on a countable set, are obtained.

The order completeness of some spaces of vector-valued functions

1974 ◽  
Vol 11 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Donald I. Cartwright
Keyword(s):  
Banach Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Banach Lattices ◽  
Nuclear Operators ◽  
Order Completeness ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Order Intervals ◽  
Vector Valued

Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.

scholarly journals Conditions of unicity of the best non-symmetric $L_1$-approximant for continuous vector-valued functions by one-dimensional subspace

2012 ◽  
Vol 20 ◽  
pp. 129
Author(s):  
M.Ye. Tkachenko ◽  
V.M. Traktyns'ka
Keyword(s):  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Necessary And Sufficient Conditions ◽  
Continuous Vector ◽  
One Dimensional ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha};\overline{\beta})$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

scholarly journals Conditions of unicity of the best non-symmetric $L_1$-approximant

2013 ◽  
Vol 21 ◽  
pp. 81
Author(s):  
Yu.S. Zagorul'ko ◽  
M.Ye. Tkachenko ◽  
V.M. Traktyns'ka
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuous Vector ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha},\overline{\beta})$-approximant with coefficient constraints for the continuous vector-valued functions on a metric compact are obtained.

scholarly journals Further results on images of metric spaces

2015 ◽  
Vol 98 (112) ◽  
pp. 179-191
Author(s):  
Van Dung
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Continuous ◽  
Locally Separable Metric Spaces ◽  
Necessary And Sufficient ◽  
Separable Metric Space

We introduce the notion of an ls-?-Ponomarev-system to give necessary and sufficient conditions for f:(M,M0) ? X to be a strong wc-mapping (wc-mapping, wk-mapping) where M is a locally separable metric space. Then, we systematically get characterizations of weakly continuous strong wc-images (wc-images, wk-images) of locally separable metric spaces by means of certain networks. Also, we give counterexamples to sharpen some results on images of locally separable metric spaces in the literature.

Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

2018 ◽  
Vol 24 (1) ◽  
pp. 45-54
Author(s):  
Aleksandra Stasiak
Keyword(s):  
Partial Order ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Polyhedral Cone ◽  
Directional Derivatives ◽  
Pareto Minima ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Derivatives Of

Abstract Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

scholarly journals Interchange of vector valued integrals when the measures are Bochner or Pettis indefinite integrals

1979 ◽  
Vol 20 (2) ◽  
pp. 199-206 ◽  
Author(s):  
Andre de Korvin ◽  
Charles E. Roberts
Keyword(s):  
Sufficient Conditions ◽  
Cross Product ◽  
Necessary And Sufficient Conditions ◽  
Product Measure ◽  
The Cross ◽  
Necessary And Sufficient ◽  
Vector Valued

Necessary and sufficient conditions for the interchange of two Bochner integrals and for the interchange of two Pettis integrals are obtained. These conditions are different from those generally required in classical Fubini theorems since they do not require the construction of the cross product measure. The proof makes use of the Vitali-Hahn-Saks Theorem. It should be noted that while Fubini theorems use the cross product measure, one of the difficulties encountered is that the product measure fails to be countable additive – this is pointed out in M. Bhaskara Rao (Indiana Univ. Math. J. 21 (1972), 847–848) and Charles Swartz (Bull. Austral. Math. Soc. 8 (1973), 359–366). Most applications require the interchange of the two integrals rather than integration with respect to the product measure.

A characterization of the set of local martingale measures

2018 ◽  
Vol 18 (05) ◽  
pp. 1850042 ◽  
Author(s):  
Abdelkarem Berkaoui
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Martingale ◽  
Probability Measures ◽  
Martingale Measures ◽  
Necessary And Sufficient ◽  
Adapted Process ◽  
Vector Valued

We generalize the results of [1] to continuous time case by stating necessary and sufficient conditions on a set of probability measures to be the set of local martingale measures for a vector valued, locally bounded and adapted process.

Analogs of Fricke's theorems for analytic vector-valued functions in the unit ball having bounded L-index in joint variables.

2019 ◽  
Vol 33 ◽  
pp. 16-26 ◽  
Author(s):  
Vitalina Baksa ◽  
Andriy Bandura ◽  
Oleg Skaskiv
Keyword(s):  
Unit Ball ◽  
Vector Function ◽  
Sufficient Conditions ◽  
Maximum Modulus ◽  
Function Class ◽  
Analytic Vector ◽  
Continuous Vector ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, we present necessary and sufficient conditions of boundedness of $\mathbb{L}$-index in joint variables for vector-functions analytic in the unit ball, where $\mathbf{L}=(l_1,l_2): \mathbb{B}^2\to\mathbb{R}^2_+$ is a positive continuous vector-function, $\mathbb{B}^2=\{z\in\mathbb{C}^2: |z|=\sqrt{|z_1|^2+|z_2|^2}\le 1\}.$ Particularly, we deduce analog of Fricke's theorems for this function class, give estimate of maximum modulus on the skeleton of bidisc. The first theorem concerns sufficient conditions. In this theorem we assume existence of some radii, for which the maximum of norm of vector-function on the skeleton of bidisc with larger radius does not exceed maximum of norm of vector-function on the skeleton of bidisc with lesser radius multiplied by some costant depending only on these radii. In the second theorem we show that boundedness of $\mathbf{L}$-index in joint variables implies validity of the mentioned estimate for all radii.

scholarly journals Lagrangian conditions for a nonsmooth vector-valued minimax

1998 ◽  
Vol 65 (2) ◽  
pp. 163-175
Author(s):  
B. D. Craven ◽  
D. V. Luu
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Jacobians ◽  
Necessary And Sufficient ◽  
Vector Valued

AbstractLagrangian necessary and sufficient conditions for a nonsmooth vector-valued minimax in terms of Clarke's generalized Jacobians are established under suitable invexity hypotheses.

Sign in / Sign up

Export Citation Format

Share Document