IJPAM: Volume 26, No. 2 (2006)

FIXED POINTS FOR WEAK COMPATIBLE TYPE AND
PARAMETRICALLY $\phi (\epsilon,\delta;a)$-CONTRACTION MAPPINGS

H.K. Pathak$^1$, R.K. Verma$^{2}$, S.M. Kang$^{3}$, M.S. Khan$^{4}$
$^{1}$Department of Mathematics
Kalyan Mahavidyalaya
Bhilai Nagar-490006, C.G., INDIA
$^1$e-mail: hkpathak@sify.com
$^{2}$Department of Mathematics
Govt. C.L.C. College
Patan, Distt.-Durg -491111, C.G., INDIA
$^{3}$Department of Mathematics
Research Institute of Natural Science
Gyengsang National University
#900 Gazwa-Dong, Chinju 660-701, KOREA
e-mail: smkang@nongae.gsnu.ac.kr
$^{4}$Department of Mathematics and Computing
Sultan Qaboos University
P.O.Box 36, Postal Code 123
Alkhod, Muscat, SULTANATE OF OMAN
e-mail: mohammad@squ.edu.om


Abstract.In this paper, we introduce the notion of parametrically $\phi (\epsilon,\delta;a)$-contraction mappings. In the sequel, we obtain common fixed point and coincidence results for family of four self-mappings of a metric space satisfying weak compatibility and parametrically $\phi (\epsilon,\delta;a)$-contractions. Another coincidence and common fixed point result is obtained for parametrically $\phi (\epsilon,\delta;a)$-contraction on star-shaped compact subsets of a normed linear space $X$ satisfying weak compatible conditions on $X$. Our results generalize the result of Jungck [4], Pathak et al [15], etc.

Received: November 28, 2005

AMS Subject Classification: 54H25, 47H10

Key Words and Phrases: common fixed point,coincidence point, $(\epsilon,\delta;a)$-contraction mappings, parametrically $\phi (\epsilon,\delta;a)$-contraction mappings, star-shaped, weak compatibile mappings

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2