Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity.
A study of boundedness in probabilistic normed spaces
✍ Scribed by Bernardo Lafuerza-Guillén; Carlo Sempi; Gaoxun Zhang
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 304 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this paper, we introduce the concept of probabilistic contractor couple in probabilistic normed spaces and discuss the existence of solution for nonlinear equations of fuzzy mappings and the convergence of sequences generated by the algorithms in Menger probabilistic normed spaces.
The concept of orthogonality in normed linear spaces has been studied extensively by BIRKHOFF [3], JAMES IS], [7], [8], and the present authors [l], 151, among others. The most natural notion of orthogonality arises in the case where there is an inner product (-, -) compatible with the norm 11. 11 o