Hostname: page-component-7bb8b95d7b-qxsvm Total loading time: 0 Render date: 2024-09-14T03:42:54.834Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Class of Multivalued Mappings in Banach Spaces

Published online by Cambridge University Press:  20 November 2018

C. J. Rhee
C. J. Rhee*
Affiliation:
Wayne State University, Detroit, Michigan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A. Granas [4] has studied single-valued compact vector fields in Banach spaces. In [3], he extended the fixed point theorems of Roth, Boknenblust and Karlin to the case of multi-valued functions. Closely following [4], we give here some general theorems in a class of multi-valued functions in Banach spaces.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 387 - 393
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Borges, C. J. R., On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16.Google Scholar
2. Borges, C. J. R., A study of multivalued functions, Pacific J. Math. 23 (1967), 451-461.Google Scholar
3. Granas, A., Theorem on antipodes and theorems on fixedpoints for a certain class of multivalued mappings in Banach spaces, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 7 (1959), 271-275.Google Scholar
4. Granas, A., The theory of compact vector fields and some of its applications to topology of functional spaces, Rozprawy Mat. XXX, Inst. Math. Acad. Polon. Sci., 1962.Google Scholar
5. Granas, A., and Jawarowski, J. W., Some theorems on multivalued mappings of subsets of the Euclidean space, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 7 (1959), 277-283.Google Scholar
6. Kakutani, S., A generalization of Brouwer's fixed point theorem, Duke Math. J. 8 (1941).Google Scholar
7. Rothe, E., Theorie der Ordnung und der Vektorfelder in Banachschen Raumen, Compositio Math. 5 (1937), 177-197.Google Scholar