Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0428265
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)

  • [1] Jörg Blatter, Grothendieck spaces in approximations theory, Mem. Amer. Math. Soc. No. 120 (1972). MR 0493107 (58:12143)
  • [2] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464. MR 39 #916. MR 0239559 (39:916)
  • [3] F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A71 = Indag. Math. 30 (1968), 27-35. MR 37 #5743. MR 0230180 (37:5743)
  • [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 mapping, J. London Math. Soc. 37 (1962), 74-79. MR 24 #A2936. MR 0133102 (24:A2936)
  • [6] Chi Song Wong, Fixed point theorems for nonexpansive mappings, Ph.D. Thesis, Univ. of Illinois, Urbana, Illinois, 1969.
  • [7] -, Subadditive functions, Pacific J. Math. 36 (1971), 549-551. MR 43 #4974. MR 0279251 (43:4974)
  • [8] -, Fixed point theorems for nonexpansive mappings, J. Math. Anal. Appl. 37 (1972), 142-150. MR 45 #2691. MR 0293614 (45:2691)
  • [9] -, A fixed point theorem for a class of mappings, Math. Ann. 204 (1973), 97-103. MR 51 #4206. MR 0367964 (51:4206)
  • [10] -, On Dugundji's notion of positive definiteness, Proc. Amer. Math. Soc. 46 (1974), 443-450. MR 0418076 (54:6120)

Similar Articles

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: http://dx.doi.org/10.1090/S0002-9939-1977-0428265-8
PII: S 0002-9939(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