International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 681-693

Common fixed points of biased maps of type (A) and applications

H. K. Pathak,1 Y. J. Cho,2 and S. M. Kang2

1Department of Mathematics, Kalyan Mahavidyalaya, Bhilai Nagar, M.P. 490 006, India
2Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea

Received 22 November 1996; Revised 18 August 1997

Copyright © 1998 H. K. Pathak et al. 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.


A generalization of compatible maps of type (A) called “biased maps of type (A)” is introduced and used to prove fixed point theorems for certain contractions of four maps. Extensions of known results are thereby obtained, i.e., the results of Pathak, Prasad, Jungck et al. are improved. Some problems on convergence of self-maps and fixed points are also discussed. Further, we use our main results to show the existence of solutions of nonlinear integral equations.