A bound for the modulus of continuity for metric projections in a uniformly convex and uniformly smooth Banach space

Journal of Approximation Theory

Volumn 85, Issue 3, 1996, Pages 237-249

  Alber, Ya I ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030167057     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0040     Document Type: Article

References (20)

1. 1. YA. I. ALBER, Metric and generalized projection operators in Banach spaces: properties and applications, in "Theory and Applications of Nonlinear Operators of Monotone and Accretive Types" (A. Kartsatos, Ed.), pp. 15-50, Marcel Dekker, 1996. E-preprint funct-an/9311001.
2. 2. YA. I. ALBER, The regularization method for variational inequalities with nonsmooth unbounded operator in Banach space, Appl. Math. Lett. 6 (1993), 63-68.
3. 3. YA. I. ALBER, The penalty method for variational inequalities with nonsmooth unbounded operator in Banach space, Numer. Funct. Anal. Optim. 16 (1995), 1111-1125.
4. 4. YA. I. ALBER AND A. I. NOTIK, On some estimates for projection operator in Banach space, Comm. Appl. Nonlinear Anal. 2 (1995), 47-56.
5. 5. YA. I. ALBER AND A. I. NOTIK, Geometric properties of Banach spaces and approximate methods for solving nonlinear operator equations, Soviet Math. Dokl. 29 (1984), 611-615.
6. 6. YA. I. ALBER AND A. I. NOTIK, Parallogram inequalities in Banach spaces and some properties of a duality mapping, Ukrainian Math. J. 40 (1988), 650-652.
7. 7. B. O. BJORNESTAL, Local Lipschitz continuity of the metric projection operator, in "Approximation Theory," Vol. 4, pp. 43-53, Stefan Banach Internat. Math. Center Publication, Warsaw, 1979.
8. 8. D. BUTNARIU AND Y. CENSOR, Strong convergence of almost simultaneous block-iterative projection methods in Hilbert spaces, J. Comput. Appl. Math. 53 (1994), 33-42.
9. 9. D. BUTNARIU AND S. D. FLAM, Strong convergence of expected-projection methods in Hilbert spaces, Numer. Funct. Anal. Optim. 16 (1995), 601-637.
10. 10. F. DEUTSCH, The method of alternating orthogonal projections, in "Approximation Theory, Spline Functions and Applications" (S. P. Singh, Ed.), pp. 105-121, Kluwer Academic, Dordrecht, 1992.
11. 11. F. DEUTSCH, doctoral thesis, Brown University, 1965.
12. 12. T. FIGIEL, On the moduli of convexity and smoothness, Studia Math. 56 (1976), 121-155.
13. 13. C. FRANCHETTI AND W. LIGHT, The alternating algorithm in uniformly convex spaces, J. London Math. Soc. (2) 29 (1984), 545-555.
14. 14. R. B. HOLMES, "A Course on Optimization and Best Approximation," Springer-Verlag, Berlin/Heidelberg/New York, 1972.
15. 15. J. LINDENSTRAUSS AND L. TZAFRIRI, "Classical Banach Spaces, II," Springer-Verlag, Berlin/Heidelberg/New York, 1979.
16. 16. J.-L. LIONS, "Quelques méthodes de résolution des problèmes aux limites non linéaires," Dunod Gauthier-Villars, Paris, 1969.
17. 17. A. I. NOTIK, Properties of a duality mapping with a scale function, Soviet Math. 29 (1985), 96-98.
18. 18. G. S. RUBENSTEIN, On an extremal problem in a linear normed space, Sibirsk. Mat. Zh. 6 (1965), 711-714. [In Russian]
19. 19. Z. XU AND G. F. ROACH, On the uniform continuity of metric projections in Banach spaces, Approx. Theory Appl. 8 (1992), 11-19.
20. 20. E. H. ZARANTONELLO, Projections on convex sets in Hilbert space and spectral theory, in "Contributions to Nonlinear Functional Analysis" (E. H. Zarantonello, Ed.), Academic Press, New York/London, 1972.