Polynomial selections and separation by polynomials

Szymon Wąsowicz

Studia Mathematica (1996)

  • Volume: 120, Issue: 1, page 75-82
  • ISSN: 0039-3223

Abstract

top
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.

How to cite

top

Wąsowicz, Szymon. "Polynomial selections and separation by polynomials." Studia Mathematica 120.1 (1996): 75-82. <http://eudml.org/doc/216322>.

@article{Wąsowicz1996,
abstract = {K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.},
author = {Wąsowicz, Szymon},
journal = {Studia Mathematica},
keywords = {separation theorem; set-valued function; selection; n-convex function; n-concave function; affine function; Helly's theorem; Lagrange interpolating polynomial; set-valued functions; Lagrange interpolation polynomial; selections; separation by polynomials; affine functions; -convex function; -concave function},
language = {eng},
number = {1},
pages = {75-82},
title = {Polynomial selections and separation by polynomials},
url = {http://eudml.org/doc/216322},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Wąsowicz, Szymon
TI - Polynomial selections and separation by polynomials
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 1
SP - 75
EP - 82
AB - K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
LA - eng
KW - separation theorem; set-valued function; selection; n-convex function; n-concave function; affine function; Helly's theorem; Lagrange interpolating polynomial; set-valued functions; Lagrange interpolation polynomial; selections; separation by polynomials; affine functions; -convex function; -concave function
UR - http://eudml.org/doc/216322
ER -

References

top
  1. [1] E. Behrends and K. Nikodem, A selection theorem of Helly type and its applications, Studia Math. 116 (1995), 43-48. Zbl0847.52004
  2. [2] Z. Ciesielski, Some properties of convex functions of higher orders, Ann. Polon. Math. 7 (1959), 1-7. Zbl0128.05704
  3. [3] K. Nikodem and S. Wąsowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math. 49 (1995), 160-164. Zbl0815.39010
  4. [4] T. Popoviciu, Les Fonctions Convexes, Hermann, Paris, 1944. Zbl0060.14911
  5. [5] T. Popoviciu, Sur quelques propriétés des fonctions d'une variable réelle convexes d'ordre supérieur, Mathematica (Cluj) 8 (1934), 1-85. Zbl0009.05901
  6. [6] A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973. Zbl0271.26009
  7. [7] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964. 
  8. [8] S. Wąsowicz, On affine selections of set-valued functions, J. Appl. Anal. 1 (1995), 173-179. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.