On some topological problems arising from maps of contractive type
Authors:
Kok Keong Tan and Chi Song Wong
Journal:
Proc. Amer. Math. Soc. 62 (1977), 167-172
MSC:
Primary 54C30; Secondary 54H25
DOI:
https://doi.org/10.1090/S0002-9939-1977-0428265-8
MathSciNet review:
0428265
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Characterizations of sequentially complete and of countably compact subsets of a uniform space are obtained. Applications to fixed point theory and coincidence theory are given.
- [1] Jörg Blatter, Grothendieck spaces in approximation theory, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 120. MR 0493107
- [2] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464. MR 0239559, https://doi.org/10.1090/S0002-9939-1969-0239559-9
- [3] Felix E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math. 30 (1968), 27–35. MR 0230180
- [4] J. Dugundji, Positive definite functions and coincidences, Séminaire de Mathématique Superieures (Fixed Point Theory and its Applications), Université de Montréal, June 1973.
- [5] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74–79. MR 0133102, https://doi.org/10.1112/jlms/s1-37.1.74
- [6] Chi Song Wong, Fixed point theorems for nonexpansive mappings, Ph.D. Thesis, Univ. of Illinois, Urbana, Illinois, 1969.
- [7] Chi Song Wong, Subadditive functions, Pacific J. Math. 36 (1971), 549–551. MR 0279251
- [8] Chi Song Wong, Fixed point theorems for nonexpansive mappings, J. Math. Anal. Appl. 37 (1972), 142–150. MR 0293614, https://doi.org/10.1016/0022-247X(72)90263-6
- [9] Chi Song Wong, A fixed point theorem for a class of mappings, Math. Ann. 204 (1973), 97–103. MR 0367964, https://doi.org/10.1007/BF01433408
- [10] Chi Song Wong, On Dugundji’s notion of positive definiteness, Proc. Amer. Math. Soc. 46 (1974), 443–450. MR 0418076, https://doi.org/10.1090/S0002-9939-1974-0418076-9
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C30, 54H25
Retrieve articles in all journals with MSC: 54C30, 54H25
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1977-0428265-8
Keywords:
Coincidence,
compactness,
completeness,
countable compactness,
fixed point,
Hausdorff pseudo-metric,
lower semicontinuity,
positive definiteness,
sequential completeness,
uniformity
Article copyright:
© Copyright 1977
American Mathematical Society
