IJPAM: Volume 19, No. 2 (2005)

FIXED POINTS OF MULTIVALUED
MAPPINGS IN D-METRIC SPACES

M. Ashraf$^1$, B. Ahmad$^2$
$^1$Centre for Advanced Studies in Pure and Applied Mathematics
Bahauddin Zakariya University
Multan, 60800, PAKISTAN
e-mail: ashrafatd@yahoo.com
$^2$Department of Mathematics
King Abdul Aziz University
Jeddah, SAUDI ARABIA


Abstract.Multivalued mappings in D-metric spaces were introduced by B.C. Dhage [#!4!#]. He defined the D-metric version of Hausdorff metric and proved some results. In this paper, we generalize the triangle contraction principle to set-valued mappings in D-metric spaces by defining Hausdorff D-metric in a different way. Consequently, the results so obtained are interesting and different from those of Dhage [#!4!#]. We extend the results of H. Kaneko [#!26!#], [#!30!#] and B.C. Dhage, A.M. Pathan and B.E. Rhoades [#!6!#] for multivalued mappings in the setting of D-metric spaces.

Received: December 30, 2004

AMS Subject Classification: 47H10, 54H25

Key Words and Phrases: D-metric space, fixed point, multivalued mapping, Hausdorff D-metric

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 2