# A characterization of reflexive spaces by means of continuous approximate selections for metric projections

@article{Zhivkov1989ACO, title={A characterization of reflexive spaces by means of continuous approximate selections for metric projections}, author={N. V. Zhivkov}, journal={Journal of Approximation Theory}, year={1989}, volume={56}, pages={59-71} }

## 6 Citations

Selections For Metric Projections

- Mathematics
- 1992

A review is given of conditions which characterise when the metric projection onto a proximinal subspace of a normed linear space has a selection which is continuous, (pointwise) Lipschitz…

Semi-continuity Properties of Metric Projections

- Mathematics
- 2014

This chapter presents some selected results regarding semi-continuity of metric projections onto closed subspaces of normed linear spaces. Though there are several significant results relevant to…

Metric Projections in Spaces of Integrable Functions

- Mathematics
- 1995

The paper is concerned with the calculation of the derived mapping of the metric projection onto a finite dimensional subspace of a space of integrable functions. Abstract results for quotient spaces…

Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

- MathematicsJ. Approx. Theory
- 2002

A number of semicontinuity concepts and the relations between them are discussed and geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dimensional subspace has a continuous C"0(T) and L"1(@m).

## References

SHOWING 1-10 OF 18 REFERENCES

Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections

- Mathematics
- 1983

Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection…

Reflexivity and the sup of linear functionals

- Mathematics
- 1972

A relatively easy proof is given for the known theorem that a Banach space is reflexive if and only if each continuous linear functional attains its sup on the unit ball. This proof simplifies…

Geometry of Banach Spaces: Selected Topics

- Mathematics
- 1975

Support functionals for closed bounded convex subsets of a Banach space.- Convexity and differentiability of norms.- Uniformly convex and uniformly smooth Banach spaces.- The classical renorming…

Nonexistence of continuous selections of the metric projection for a class of weak Chebyshev spaces

- Mathematics
- 1980

The class 3 of all those n-dimensional weak Chebyshev subspaces of C[a, b] whose elements have no zero intervals is considered. It is shown that there does not exist any continuous selection of the…

Characterization of Continuous Selections for the Metric Projection for Generalized Splines

- Mathematics
- 1980

In this paper we give a characterization of those generalized spline spaces which admit continuous selections for the metric projection. We denote by generalized splines those weak Chebyshev spaces…

Nonexistence of Continuous Selections of the Metric Projection and weak Chebyshev Systems

- Mathematics
- 1980

We show that an n-dimensional subspace G of $C[a,b]$ which admits a continuous selection for the metric projection has to be weak Chebyshev. For $C[a,b]$ this solves one part of a problem posed by…