Convergence of Pólya Algorithm and Continuous Metric Selections in Space of Continuous Functions
✍ Scribed by W. Li
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 601 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0021-9045
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✦ Synopsis
We show that one can construct a continuous selection for the metric projection in the space of continuous functions by the Pólya algorithm. Moreover, the existence of a continuous selection for the metric projection is equivalent to the stable convergence of the Pólya algorithm. 1995 Academic Press. Inc.
📜 SIMILAR VOLUMES
We introduce a linearization property for parameter dependent operators from a space of continuous functions into itself. This notion leads to a new implicit function theorem. As an application, we study the stability of the solutions of the Ž .
## Abstract Let __I__, __J__ ⊂ ℝ be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ × __J__ → ℝ, __H__ (__φ__)(__x__) ≔ __h__ (__x__, __φ__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,
Math. Nechr. 149 (1990) and (1.7) respectively, where the parameter 5 tends to 0. n W Z , 5 ) = ( 6 Z -l J I(% + 1) exp (-t2/5) d t , -JI Throughout the paper, we shall write (1.8) @A = I(% + 1) -2f(Z)'+ f ( Z -0 . 2.