International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 10, Pages 627-635

Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

S. L. Singh1 and S. N. Mishra2

1Department of Mathematics, Gurukula Kangri Vishwavidyalaya, Hardwar 249404, India
2Department of Mathematics, University of Transkei, Umtata 5100, South Africa

Received 16 February 2001; Revised 27 March 2001

Copyright © 2002 S. L. Singh and S. N. Mishra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.