IJPAM: Volume 31, No. 1 (2006)

EQUIVALENT CONDITIONS FOR
CONTRACTIVE TYPE MAPPINGS IN METRIC SPACES

Zeqing Liu$^1$, Zhenyu Guo$^2$, Shin Min Kang$^{3}$Department of Mathematics; Gyeongsang National University; Jinju, 660-701, KOREA, Soo Hak Shim$^4$ $^{1,2}$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning 116029, P.R. CHINA
$^1$e-mail: zeqingliu@dl.cn
$^2$e-mail: zhenyu-guo@163.com
$^3$Department of Mathematics
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: smkang@nongae.gsnu.ac.kr
$^{3,4}$Research Institute of Natural Science
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: math@nongae.gsnu.ac.kr


Abstract.In this paper the pairwise equivalences for 30 contractive conditions involving $(\varphi,p,q)$-contractive type mappings in metric spaces are established, which generalize and improve the equivalence results given by Jachymski.

Received: July 20, 2006

AMS Subject Classification: 54H25

Key Words and Phrases: equivalence, contractive type mapping, metric space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 1