Access the full text.
Sign up today, get DeepDyve free for 14 days.
Acta Mathematica Academiae Scientiarum Hungaricae Tomus 37 (4), (1981), 355~372. THE MODULUS OF CONINUITY OF THE SET-VALUED METRIC PROJECTION By G. GODINI (Bucharest) Introduction Let E and E~ be normed linear spaces, T: E~E~ a continuous mapping and xEE. The modulus of continuity of T at x (see e.g. [9]) is the function defined by (1) Or(X, 8) = sup {[]Zx-Tyl[: yEE, []Y-Xll <- 8} (8 >= 0). For McE, the (strong) modulus of continuity of T on M (see e.g. [9]) is defined by (2) E2r(M; 8) = sup {aT(x, 8): xEM} (8 >- 0). If G is a linear subspace of the normed linear space E and xEE, we denote by Po(x) the set of all best approximations of x out of G, i.e., Po(x) = {g0EG: [[X-goll = inf [lx-g[[}. oEG The (set-valued) mapping x~Po(x) is called the (set-valued) metric projection of E onto G. Let us also denote (3) Do = {xEE: Pa(x) #~} (4) F~ = {xEDo: PG(x) is a singleton}. G is called a proximinal (respectively Chebyshev) subspace of E if Da=E (re- spectively FG=E). If Po(x)#~, we shall sometimes denote an element of Po(x) by pa(x). S. B. STE~KIN posed the problem
Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals
Published: Jun 18, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.