International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 341-346
doi:10.1155/S0161171201006822

On mappings with diminishing orbital diameters

Zeqing Liu1 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 14 February 2001

Copyright © 2001 Zeqing Liu and Shin Min Kang. 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.

Abstract

We introduce the concepts of ∗-diminishing orbital diameters and diminishing orbital diameters for a pair (f,g) of self mappings in metric spaces and prove common fixed point theorems for these mappings. The results obtained in this paper extend properly the result of Fisher (1978).